Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1-4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws.     

Modeling of the acoustic response from contrast agent microbubbles near a rigid wall

In ultrasonic targeted imaging, specially designed encapsulated microbubbles are used, which are capable of selectively adhering to the target site in the body. A challenging problem is to distinguish the echoes from such adherent agents from echoes produced by freely circulating agents. In the present paper, an equation of radial oscillation for an encapsulated bubble near a plane rigid wall is derived. The equation is then used to simulate the echo from a layer of contrast agents localized on a wall. The echo spectrum of adherent microbubbles is compared to that of free, randomly distributed microbubbles inside a vessel, in order to examine differences between the acoustic responses of free and adherent agents. It is shown that the fundamental spectral component of adherent bubbles is perceptibly stronger than that of free bubbles. This increase is accounted for by a more coherent summation of echoes from adherent agents and the acoustic interaction between the agents and the wall. For cases tested, the increase of the fundamental component caused by the above two effects is on the order of 8-9 dB. Bubble aggregates, which are observed experimentally to form near a wall due to secondary Bjerknes forces, increase the intensity of the fundamental component only if they are formed by bubbles whose radii are well below the resonant radius. If the formation of aggregates contributes to the growth of the fundamental component, the increase can exceed 17 dB. Statistical analysis for the comparison between adhering and free bubbles, performed over random space bubble distributions, gives p-values much smaller than 0.05.     

Translational instability of a spherical bubble in a standing ultrasound wave

Translational bubble dynamics is much less studied than the dynamics of radial bubble oscillation, while in many scientific and engineering applications the control of space location of cavitation bubbles is of great practical importance. This paper aims at the theoretical study of various aspects of the translational motion of a spherical gas bubble in a high-frequency standing wave. In particular, it is shown that the translational instability that gives rise to the reciprocal translation of a spherical bubble between the pressure antinode and the pressure node is caused by the hysteresis in the main resonance of the bubble. Different types of translational trajectories that can occur in a standing wave are illustrated by numerical simulations. A general classification of the observed translational trajectories is proposed.     

Use of ultrasonics in shear layer cavitation control

In this paper we report results from some investigations on the use of ultrasonics in controlling hydrodynamic cavitation in the shear layer downstream of a sudden expansion. Control of this type of cavitation has been achieved by modulating the local pressure that was experienced by a nucleus present in the shear layer. This modulation was made possible by using a piezoelectric device, termed as Ultrasonic Pressure Modulator (UPM). The performance of UPM has been studied at different dissolved gas concentrations with electrolysis bubbles as nuclei. Control of cavitation due to natural nuclei has also been attempted. Efficiency of UPM, in reducing cavitation, was seen to be dependent on the driving frequency employed. Experimental and numerical studies have been conducted to bring out the physics behind this approach of cavitation control. Different measures of cavitation control have been identified and some possible applications of this method have also been outlined.     

The Rayleigh-Plesset equation in terms of volume with explicit shear losses

The most common nonlinear equation of motion for the damped pulsation of a spherical gas bubble in an infinite body of liquid is the Rayleigh-Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid (the so-called ‘radius frame’). However over the past few decades several important analyses have been based on a heuristically derived small-amplitude expansion of the Rayleigh-Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. So common is the use of this equation in some fields that the inherent differences between it and the ‘radius frame’ Rayleigh-Plesset equation are not emphasised, and it is important in comparing the results of the two equations to understand that they differ both in terms of damping, and in the extent to which they neglect higher order terms. This paper highlights these differences. Furthermore, it derives a ‘volume frame’ version of the Rayleigh-Plesset equation which contains exactly the same basic physics for dissipation, and retains terms to the same high order, as does the ‘radius frame’ Rayleigh-Plesset equation. Use of this equation will allow like-with-like comparisons between predictions in the two frames.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller-Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 mum diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

Impact of acoustic pressure on ambient pressure estimation using ultrasound contrast agent

Local blood pressure measurements provide important information on the state of health of organs in the body and can be used to diagnose diseases in the heart, lungs, and kidneys. This paper presents an approach for investigating the ambient pressure sensitivity of a contrast agent using diagnostic ultrasound. The experimental setup resembles a realistic clinical setup utilizing a single array transducer for transmit and receive. The ambient pressure sensitivity of SonoVue (Bracco, Milano, Italy) was measured twice using two different acoustic driving pressures, which were selected based on a preliminary experiment. To compensate for variations in bubble response and to make the estimates more robust, the relation between the energy of the subharmonic and the fundamental component was chosen as a measure over the subharmonic peak amplitude. The preliminary study revealed the growth stage of the subharmonic component to occur at acoustic driving pressures between 300 and 500 kPa. Based on this, the pressure sensitivity was investigated using a driving pressure of 485 and 500 kPa. At 485 kPa, a linear pressure sensitivity of 0.42 dB/kPa was found having a linear correlation coefficient of 0.94. The second measurement series at 485 kPa showed a sensitivity of 0.41 dB/kPa with a correlation coefficient of 0.89. Based on the measurements at 500 kPa, this acoustic driving pressure was concluded to be too high causing the bubbles to be destroyed. The pressure sensitivity for these two measurement series were 0.42 and 0.25 dB/kPa with linear correlation coefficients of 0.98 and 0.93, respectively.     

Directing ultrasound at the cemento-enamel junction (CEJ) of human teeth: I. Asymmetry of ultrasonic path lengths

The diagnosis of degenerative changes in human teeth is of general interest because early detections can avoid greater health problems and further weakening effects. Since the wear of teeth determines their stability and lifetime in relation to the physiological load, an ultrasonic survey of any dimensional changes of the enamel layer and especially of the dentin wall thickness may be very helpful. However, an ultrasonographic diagnosis requires first to determine the anisotropic human tooth properties at clinically relevant locations and to simulate wave propagation phenomena in inhomogeneous tooth models with proper dimensions. The first article of a series that provides modular data of mineralized tissues in human teeth at the cemento-enamel junction (CEJ) deals with an ultrasonic method for measuring the asymmetry of dimensional characteristics of extracted human teeth and their ultrasonic path lengths (UPL). Heavily attenuating tooth halves were investigated with respect to the symmetry of normal and inclined oppositely directed radial ultrasonic paths. The measured UPLs ranged from 1.2 mm to 4.4 mm. The relative difference in inclined UPLs between the left and the right tooth halves reaches almost 30%. This reveals a large asymmetry. The mean difference of angles that represent fastest path lengths was 2.2+/-8.1 degrees, which indicates large asymmetry and anisotropy. Several aspects, which are required for a proper integration of asymmetric data into models designed for medical element engineering and simulation (MEES), are discussed.     

Ultrasonic scattering cross sections of shell-encapsulated gas bubbles immersed in a viscoelastic liquid: first and second harmonics

The oscillations of gas bubbles, without shell, immersed in viscoelastic liquids and driven by an acoustic wave have been the subject of several investigations. They demonstrate that the viscosity coefficient and the spring constant of the liquid have significant influence on the scattering cross section of the gas bubble. For shell-encapsulated gas bubbles, the investigations have been concentrated to bubbles immersed in a pure viscous liquid. This present work computes the ultrasonic scattering cross section, first and second harmonics, of shell-encapsulated gas bubbles immersed in a viscoelastic liquid. The theoretical model of the bubble oscillation is based on the generalized Rayleigh-Plesset equation of motion of a spherical cavity immersed in a viscoelastic liquid represented by a three-parameter linear Oldroyd model. The scattering cross section is computed for Albunex type of bubble (shell thickness=15 nm, shell shear viscosity=1.77 Pas, shell modulus of rigidity=88.8 MPa) irradiated by a 3.5 MHz ultrasonic pressure wave with an amplitude of 30 kPa. The results demonstrate that encapsulated bubbles respond independently of the surrounding liquid being pure viscous or viscoelastic as long as the surrounding liquid shear viscosity is as low as 10(-3) Pas. Nevertheless, for higher shear viscosities, the bubble responds differently if the surrounding liquid is pure viscous or viscoelastic. In general, the scattering cross sections of first and second harmonics are larger for the viscoelastic liquid.     

Estimation of critical and viscous frequencies for Biot theory in cancellous bone

The use of Biot theory for modelling ultrasonic wave propagation in porous media involves the definition of a "critical frequency" above which both fast and slow compressional waves will, in principle, propagate. Critical frequencies have been evaluated for healthy and osteoporotic cancellous bone filled with water or marrow, using data from the literature. The range of pore sizes in bone gives rise to a critical frequency band rather than a single critical frequency, the mean of which is lower for osteoporotic bone than normal bone. However, the critical frequency is a theoretical concept and previous researchers considered a more realistic "viscous frequency" above which both fast and slow waves may be experimentally observed. Viscous frequencies in bone are found to be several orders of magnitude greater than calculated critical frequencies. Whereas two waves may well be observed at all ultrasonic frequencies for water-filled cancellous bone at 20 degrees C, it is probable megahertz frequencies would be needed for observation of two waves in vivo.     

Effect of adhesion force between crack planes on subharmonic and DC responses in nonlinear ultrasound

Subharmonic and DC responses in nonlinear ultrasound have been expected as a possible means of detecting closed cracks. Recently, it has been reported that subharmonics in a closed crack markedly increases above a certain input wave amplitude. Such a phenomenon is called "threshold behavior". However, the mechanism of threshold behavior has yet to be elucidated. To clarify this, we introduced adhesion force as a short-range force into the previous analytical model, which expresses the nonlinear contact vibrations of crack planes with intense ultrasound and provides a DC displacement as an approximation of the subharmonic response. Consequently, upward convex curves of displacement against input wave amplitude above the threshold were reproduced for the first time. The validity of the derived analytical solution is discussed by comparison with experimentally observed subharmonics.     

A comparison measurement of nonlinear ultrasonic waves in tubes by a microphone and by an optical interferometric probe

This paper deals with the analysis of ultrasonic fields inside waveguides generated by ultrasonic waves of high amplitude. These waves behave nonlinearly, so it is not possible to use standard linear equations to describe their behaviour. Therefore, we started with an experimental determination of the acoustic pressure of air in glass tubes. We chose two methods of measurement--by a microphone and by an optical interferometric probe. The conventional method by a microphone creates numerous problems, which can be avoided by using an optical method, a heterodyne laser interferometer.     

Measurement of the thorium-228 activity in solutions cavitated by ultrasonic sound

We show that cavitation of a solution of thorium-228 in water does not induce its transformation at a faster rate than the natural radioactive decay. We measured the activity of a thorium-228 solution in water before, and after, it was subjected to a cavitation at 44 kHz and 250 W for 90 min in order to observe any change in the thorium half-life. The results were compared to the original activity of the sample and we observed no change. Our results and conclusions conflict with those in a recent paper by F. Cardone et al. [1].     

The role of energy density and acoustic cavitation in shock wave lithotripsy

Today a high percentage of urinary stones are successfully treated by extracorporeal shockwave lithotripsy (SWL); however, misconceptions regarding fragmentation mechanisms, as well as treatment parameters like dose, applied energy and focal area are still common. A main stone comminution mechanism during SWL is acoustic cavitation. The objective of this study was to analyze the influence of cavitation and energy density on stone fragmentation. A research lithotripter was used to expose a large set of artificial kidney stones to shock waves varying different parameters. Hundreds of pressure records were used to calculate the energy density of the lithotripter at different settings. Results indicate that energy density is a crucial parameter and that better SWL treatment outcomes could be obtained placing the calculus at a prefocal position.     

超声造影剂微泡非线性动力学响应的机理及相关应用

随着生命科学及现代医学的发展, 一体化无创精准诊疗已经日益成为人们关注的焦点问题, 而关于超声造影剂微泡的非线性效应的相关机理、动力学建模及其在超声医学领域中的应用研究也得到了极大的推动. 本文对下列课题进行了总结和讨论, 包括: 1)基于Mie散射技术和流式细胞仪对造影剂微泡参数进行定征的一体化解决方案; 2)通过对微泡包膜的黏弹特性进行非线性修正, 构建新的包膜微泡动力学模型; 3)探索造影剂惯性空化阈值与其包膜参数之间的相关性; 以及4)研究超声联合造影剂微泡促进基因/药物转染效率并有效降低其生物毒性的相关机理.     

In Vivo Monitoring of Neovascularization in Tumour Angiogenesis by Photoacoustic Tomography

Photoacoustic tomography （PAT） is presented to in vivo monitor neovascularization in tumour angiogenesis with high resolution and high contrast images in a rat. With a circular scan system, the photoacoustic signal, generated by laser pulses at a wavelength of 532nm from a Q-switched Nd：YAG laser is captured by a hydrophone with a diameter of 1 mm and a sensitivity of 850nV/Pa. The vascular structure around the rat tumour is imaged clearly, with optimal contrast, because blood has strong absorption near this wavelength. Serial noninvasive photoacoustic images of neovascularization in tumour angiogenesis are also obtained consecutively from a growing tumour implanted under the skin of a rat over a period of two weeks. This work demonstrates that PAT can potentially provide a powerful tool for tumour angiogenesis detection in cancer research. It will bring us closer to clinical applications for tumour diagnosis and treatment monitoring.     

Space distribution of harmonic mode vibration amplitudes in nonlinear finite piezoelectric transducer

Nonlinear elastic vibrations of cylindrical piezoelectric transducers are investigated both experimentally and theoretically. A particular behaviour, that relates the space distribution of the fundamental mode vibration to those of the second and third harmonic components, is observed. A simplified physical interpretation of the phenomenon is given.     

超声造影剂微气泡的包膜黏弹特性的定量表征研究

包膜黏弹特性显著影响微气泡超声造影剂的诊断及治疗应用效果. 本文结合原子力显微镜技术及声衰减特性测量提出了一种对微气泡造影剂包膜黏弹特性定量表征的新方法. 首先采用原子力显微镜技术进行机械特性分析得到包膜微气泡的有效硬度及体弹性模量; 然后测量声衰减特性, 基于微气泡动力学理论, 计算包膜微气泡的体黏度系数. 为验证方法的有效性, 实验制备了直径为1-5 μm的白蛋白包膜微气泡造影剂, 原子力显微镜测量的有效硬度和体弹性模量分别为0.149±0.012 N/m和8.31±0.667 MPa, 并与粒径无关. 声衰减特性测量和动力学理论拟合的包膜微气泡的体黏度系数为0.374±0.003 Pa·s. 该方法可推广至其他种类包膜微气泡的黏弹特性表征, 对超声造影剂的制备及其诊断和治疗应用有积极意义.     

Anomalous absorption of bulk shear sagittal acoustic waves in a layered structure with viscous fluid

It is demonstrated theoretically that the absorptivity of bulk shear sagittal waves by an ultra-thin layer of viscous fluid between two different elastic media has a strong maximum (in some cases as good as 100%) at an optimal layer thickness. This thickness is usually much smaller than the penetration depths and lengths of transverse and longitudinal waves in the fluid. The angular dependencies of the absorptivity are demonstrated to have significant and unusual structure near critical angles of incidence. The effect of non-Newtonian properties and non-uniformities of the fluid layer on the absorptivity is also investigated. In particular, it is shown that the absorption in a thin layer of viscous fluid is much more sensitive to non-zero relaxation time(s) in the fluid layer than the absorption at an isolated solid-fluid interface.