包膜黏弹特性及声驱动参数对相互作用微泡动力学行为的影响

关于多气泡相互作用的理论研究对于深入理解超声造影剂在医疗领域中的应用机理具有重要意义。本工作建立了一个2维轴对称有限元模型来研究流体环境中超声造影剂双气泡相互作用,讨论了驱动超声频率和气泡尺寸对气泡之间吸引和排斥趋势的影响,得到了气泡半径与气泡之间距离随时间变化的曲线,以及气泡周围流体速度场的细节,并且研究了气泡包膜参数(即表面张力系数和粘度系数)对气泡相互作用的影响.结果表明,相互作用中的气泡对整体的相对运动趋势由驱动频率和共振频率之间的关系决定;在超声参数固定时,气泡包膜的粘弹特性可用来调控气泡间相互作用强度。结果对实验中观察到的气泡聚集现象进行了合理解释,并为超声造影剂在医疗实践中的应用提供了基础理论支撑.     

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh-Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the “compression-only” behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2-2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20 cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30 × 10⁻⁸ kg/s to 2.63 × 10⁻⁸ kg/s for the range of bubble radii, indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the “compression-only” behavior. As an example, the results of the simulation for a 2.03 μm radius bubble insonified with a 6 cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the “compression-only” behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653-656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius.     

Resonance frequency of microbubbles: effect of viscosity

The transmitted frequency at which a gas bubble of millimeter or submillimeter size oscillates resonantly in a low-viscosity liquid is approximately equal to the undamped natural frequency (referred to as the Minnaert frequency if surface tension effects are disregarded). Based on a theoretical analysis of bubble oscillation, this paper shows that such an approximation cannot be validated for microbubbles used in contrast-enhanced ultrasound imaging. The contrast-agent microbubbles represent either encapsulated bubbles of size less than 10 microm or free (nonencapsulated) bubbles of submicron size. The resonance frequency of the microbubbles deviates significantly from the undamped natural frequency over the whole range of microbubble sizes due to the increased viscous damping coefficient. The difference between these two frequencies is shown to have a tremendous impact on the resonant backscatter by the microbubbles. In particular, the first and second harmonics of the backscattered signal from the microbubbles are characterized by their own resonance frequencies, equal to neither the microbubble resonance frequency nor the undamped natural frequency.     

Adaptive control of contrast agent microbubbles for shell parameter identification

An adaptive controller design is proposed and simulated for parameter identification and oscillation control in microbubble systems. Lyapunov's direct method and a Lyapunov-like analysis are used to show stability and convergence of trajectory tracking and parameter adaptation. The method allows for the determination of microbubble contrast agent shell thickness or material parameters in a nondestructive manner.     

Scaling of the viscoelastic shell properties of phospholipid encapsulated microbubbles with ultrasound frequency

Phospholipid encapsulated microbubbles are widely employed as clinical diagnostic ultrasound contrast agents in the 1–5 MHz range, and are increasingly employed at higher ultrasound transmit frequencies. The stiffness and viscosity of the encapsulating “shells” have been shown to play a central role in determining both the linear and nonlinear response of microbubbles to ultrasound. At lower frequencies, recent studies have suggested that shell properties can be frequency dependent. At present, there is only limited knowledge of how the viscoelastic properties of phospholipid shells scale at higher frequencies. In this study, four batches of in-house phospholipid encapsulated microbubbles were fabricated with decreasing volume-weighted mean diameters of 3.20, 2.07, 1.82 and 1.61 μm. Attenuation experiments were conducted in order to assess the frequency-dependent response of each batch, resulting in resonant peaks in response at 4.2, 8.9, 12.6 and 19.5 MHz, respectively. With knowledge of the size measurements, the attenuation spectra were then fitted with a standard linearized bubble model in order to estimate the microbubble shell stiffness S_p and shell viscosity S_f, resulting in a slight increase in S_p (1.53–1.76 N/m) and a substantial decrease in S_f (0.29 × 10⁻⁶–0.08 × 10⁻⁶ kg/s) with increasing frequency. These results performed on a single phospholipid agent show that frequency dependent shell properties persist at high frequencies (up to 19.5 MHz).     

The viscoelasticity of lipid shell and the hysteresis of subharmonic in liquid containing microbubbles

The viscoelasticity and subharmonic generation of a kind of lipid ultrasound contrast agent are investigated. Based on the measurement of the sound attenuation spectrum, the viscoelasticity of the lipid shell is estimated by use of an optimization method. Shear modulus G_S=10MPa and shear viscosity \mu _S=1.49N\cdotS/m² are obtained. The nonlinear oscillation of the encapsulated microbubble is studied with Church's model theoretically and experimentally. Especially, the dependence of subharmonic on the incident acoustic pressure is studied. The results reveal that the development of the subharmonic undergoes three stages, i.e. occurrence, growth and saturation, and that hysteresis appears in descending ramp insonation.     

Phospholipid-stabilized microbubbles: Influence of shell chemistry on cavitation threshold and binding to giant uni-lamellar vesicles

We demonstrate the feasibility of covalently linking a single microbubble to a single, giant uni-lamellar vesicle (GUV). Such a combination of GUV plus microbubble might prove useful as a new drug delivery vehicle involving microbubble cavitation-induced sonoporation of the vesicle bilayer as a release mechanism. We therefore applied the well known methodology of passive cavitation detection to measure the influence of lipid shell chemistry on inertial cavitation thresholds for externally added microbubbles. We find that cavitation threshold changes significantly with changes in either molecular weight or mole fraction of poly(ethylene glycol), historically used to impede gas dissolution and microbubble coalescence. We attribute changes in cavitation threshold to changes in microbubble resonance frequency resulting from changes in microbubble shell bending elasticity. To further demonstrate the influence of shell chemistry on microbubble behavior, we describe how several common bubble phenomena - and some new - respond to changes in lipid chain length.     

Nonlinear radial oscillations of encapsulated microbubbles subject to ultrasound: the effect of membrane constitutive law

The nonlinear radial oscillations of bubbles that are encapsulated in an elastic shell are investigated numerically subject to three different constitutive laws describing the viscoelastic properties of the shell: the Mooney-Rivlin (MR), the Skalak (SK), and the Kelvin-Voigt (KV) models are used in order to describe strain-softening, strain-hardening and small displacement (Hookean) behavior of the shell material, respectively. Due to the isotropic nature of the acoustic disturbances, the area dilatation modulus is the important parameter. When the membrane is strain softening (MR) the resonance frequency decreases with increasing sound amplitude, whereas the opposite happens when the membrane is strain hardening (SK). As the amplitude of the acoustic disturbance increases the total scattering cross section of a microbubble with a SK membrane tends to decrease, whereas that of a KV or a MR membrane tends to increase. The importance of strain-softening behavior in the abrupt onset of volume pulsations, that is often observed with small insonated microbubbles at moderately large sound amplitudes, is discussed.     

Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal,radiation and encapsulating shell damping at various excitation pressures

This study presents the fundamental equations governing the pressure dependent disipation mechanisms in the oscillations of coated bubbles. A simple generalized model (GM) for coated bubbles accounting for the effect of compressibility of the liquid is presented. The GM was then coupled with nonlinear ODEs that account for the thermal effects. Starting with mass and momentum conservation equations for a bubbly liquid and using the GM, nonlinear pressure dependent terms were derived for power dissipation due to thermal damping (Td), radiation damping (Rd) and dissipation due to the viscosity of liquid (Ld) and coating (Cd). The pressure dependence of the dissipation mechanisms of the coated bubble have been analyzed. The dissipated energies were solved for uncoated and coated 2–20 $\mathrm{\mu }\text{m}$ in bubbles over a frequency range of $0.25f_r-2.5f_r$ ($f_r$ is the bubble resonance) and for various acoustic pressures (1 kPa-300 kPa). Thermal effects were examined for air and C3F8 gas cores. In the case of air bubbles, as pressure increases, the linear thermal model looses accuracy and accurate modeling requires inclusion of the full thermal model. However, for coated C3F8 bubbles of diameter 1–8 $\mathrm{\mu }\text{m}$, which are typically used in medical ultrasound, thermal effects maybe neglected even at higher pressures. For uncoated bubbles, when pressure increases, the contributions of Rd grow faster and become the dominant damping mechanism for pressure dependent resonance frequencies (e.g. fundamental and super harmonic resonances). For coated bubbles, Cd is the strongest damping mechanism. As pressure increases, Rd contributes more to damping compared to Ld and Td. For coated bubbles, the often neglected compressibility of the liquid has a strong effect on the oscillations and should be incorporated in models. We show that the scattering to damping ratio (STDR), a measure of the effectiveness of the bubble as contrast agent, is pressure dependent and can be maximized for specific frequency ranges and pressures.     

微泡对高强度聚焦超声焦域影响的研究

微泡对高强度聚焦超声(HIFU)治疗具有增效作用,而HIFU治疗中不同声学条件下微泡对HIFU治疗焦域的影响尚不清楚。本文基于声传播方程、Yang-Church气泡运动方程、生物热传导方程、时域有限差分法(FDTD)、龙格-库塔(RK)法数值仿真研究输入功率、激励频率和气泡初始半径对HIFU在含气泡体模中形成焦域的影响,并利用含Sono Vue造影剂的仿组织体模研究进行实验验证。结果表明,增大输入功率、气泡初始半径和升高激励频率均可增大焦域,随着输入功率的增大,焦域形状可能发生变化,而随着激励频率升高和气泡初始半径的增大,焦域会向远离换能器的方向移动。     

Oscillations in collector current of a double heterostructure bipolar transistor: a quantum effect

In spite of many advantages, GaInP/GaAs/GaInP double heterostructure bipolar transistors (DHBT) suffer from the disadvantage of energy barrier to flow of carriers at the collector-base junction due to non-zero conduction band edge discontinuity which results in higher V_D,sat. To circumvent this critical problem, Liu et al. IEEE Transactions on Electron Devices, 40 , 1384-1389 (1993) have employed a set-back layer of undoped GaAs between the base and the collector. As a consequence of the set-back layer, they observed oscillations in the collector current in the forward active mode with the output voltage (V_BC), the origin of which they proposed to be the presence and absence of resonant energy levels at the energy equal to the conduction band edge, E_c, of the base. In this work, we have investigated the origin and conditions of these oscillations theoretically. Energy band balance was performed at the base-set-back layer and set-back layer-collector junctions to determine the distribution of the output voltage, V_BC, at these junctions using degenerate statistics. This calculation also provided the electric field and potential drop on the set-back layer. The parabolic E_c profiles of the base and collector depletion layers were linearized. The transmission coefficient as a function of energy was obtained using Airy and exponential function solutions to Schrödinger equation. The transmission coefficient was energy averaged for various V_BCS and thus, a transmission parameter for the collector-base junction was obtained and used in a DC I-V characteristics model. Theoretical results are in excellent agreement with the experimental results with the V_BCS at which the peaks of the collector current occurs matching closely for the first two peaks.     

Evaluation of ultrasound and microbubbles effect on pork meat during brining process

In this study combined effect of ultrasound-induced acoustic cavitation and microbubbles during meat brining on pork loin (Longissimus dorsi) was evaluated. Cylindrical shape (diameter 15 mm, height 80 mm) pork loin samples were cut and immersed in 200 g L^-1 NaCl brine and treated with the following brining methods for 180 min: static brining (SB), ultrasound assisted brining (US) and ultrasound combined with microbubbles in brine (USMB). Ultrasound was generated with 20 kHz frequency, 5,09 W/cm² maximum intensity and 100 W maximum power. Microbubbles in brine were produced by a gas–liquid mixing pump. Effect of ultrasound and microbbubles on NaCl content and diffusion in pork loin, mass balance, water binding capacity (WBC), protein denaturation and meat tissue microstructure were evaluated. The US and USMB brinings enhanced the NaCl diffusion into meat compared to meat brined under static conditions. The constant diffusion coefficient (D) model precisely described the NaCl diffusion kinetics during brinings. The ultrasound and microbbubles resulted in microscopic pores on the surface of myofibers. Decreasing WBC was observed for all brining methods. Myosin was not detectable in any of the brining methods. Denaturation temperature of actin showed a decreasing tendency with increasing brining time independently the brining methods.     

微泡对高强度聚焦超声声压场影响的仿真研究*

微泡对高强度聚焦超声(HIFU)治疗焦域具有增效作用,而HIFU治疗中不同声学条件下微泡对HIFU形成声压场的影响尚不清楚。本文基于气液混合声波传播方程、Keller气泡运动方程、时域有限差分(FDTD)法和龙格-库塔(RK)法数值仿真研究输入声压、激励频率、气泡初始空隙率和气泡初始半径对HIFU形成声压场的影响。研究结果表明,随着输入声压的增大,焦点处声压升高但焦点处最大声压与输入声压的比值减小,焦点位置几乎不变;随着激励频率和气泡初始半径的增大,焦点处声压升高且焦点位置向远离换能器方向移动;随着气泡初始空隙率的增大,焦点处声压降低且焦点位置向换能器方向移动。     

Theory of the skin effect of an electrically conducting spherical shell

Since the periodic change of the polarity of the magnetic field of a considerable number of celestial bodies is well established, the need for a theoretical treatment of this problem becomes obvious. There exists a rather voluminous literature on the skin effect in configurations of linear conductors, but practically no literature on spheres or spherical shells. First steps were taken byFanselau andLucke [1]. Here in this paper the general theory of the problem is developed. In succeeding papers the theory will be applied to two limiting cases, namely small and large bodies.     

On the absence of a density effect for inner shell ionization

It is shown that the observed absence of a density effect in inner shell ionization in solids is due to the fact that the required momentum transfer has a wavelength of the order of, or smaller than, the lattice constant, and thus cannot be transmitted to the lattice. This leads to a cut-off in the dielectric function corresponding to electronic binding energies above 1—1.5 keV, depending on the lattice constant. For more strongly bound electrons there shoul be no density effect.     

Mechanisms underlying sonoporation: Interaction between microbubbles and cells

The past several decades have witnessed great progress in “smart drug delivery”, an advance technology that can deliver genes or drugs into specific locations of patients’ body with enhanced delivery efficiency. Ultrasound-activated mechanical force induced by the interactions between microbubbles and cells, which can stimulate so-called “sonoporation” process, has been regarded as one of the most promising candidates to realize spatiotemporal-controllable drug delivery to selected regions. Both experimental and numerical studies were performed to get in-depth understanding on how the microbubbles interact with cells during sonoporation processes, under different impact parameters. The current work gives an overview of the general mechanism underlying microbubble-mediated sonoporation, and the possible impact factors (e.g., the properties of cavitation agents and cells, acoustical driving parameters and bubble/cell micro-environment) that could affect sonoporation outcomes. Finally, current progress and considerations of sonoporation in clinical applications are reviewed also.     

Drag reduction by microbubbles in turbulent flows: the limit of minute bubbles

Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking, however, making actual design quite haphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of the bubbles. Comparisons with experiments are discussed and the road ahead is sketched.