Doinikov Alexander A, Haac Jillian F, Dayton Paul A
Institute of Nuclear Problems, Belarus State University, Minsk, Belarus.
Ultrasonics. 2009 Feb;49(2):269-75. doi: 10.1016/j.ultras.2008.09.007. Epub 2008 Sep 30.
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 microm. 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 x 10(-8) kg/s to 2.63 x 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 microm 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.
本文提出了一种用于构建对比微泡零厚度包封模型的通用理论方法。该方法描述了一种程序，可将现有的体相形式的流变学定律转换为表面形式，用于修正后的瑞利 - 普莱斯方程，该方程用于控制对比微泡的径向动力学。通过使用所提出的程序，可以对不同的包封流变学定律进行测试。讨论了现有脂质包封微泡壳模型的挑战，例如壳参数对初始气泡半径的依赖性以及“仅压缩”行为。通过使用半径在1.2 - 2.5微米范围内的脂质包被微泡的实验半径 - 时间曲线，对脂质包封的流变行为进行了分析。这些曲线是针对一种研究用的磷脂包被对比剂获得的，该对比剂用20个周期、3.0 MHz、100 kPa的声脉冲进行超声照射。用将壳视为粘弹性固体的模型对实验数据进行拟合，得到在上述气泡半径范围内，壳表面粘度值从0.30×10⁻⁸ kg/s增加到2.63×10⁻⁸ kg/s。壳表面弹性模量从0.054 N/m增加到0.37 N/m。有人提出这种增加可能是由于脂质涂层具有剪切变稀和应变软化材料的特性。我们假设这些复杂的流变特性使得现有壳模型不能令人满意地描述脂质包封的动力学。在现有的壳模型中，粘性和弹性壳项具有线性形式，这意味着作用在脂质壳内的粘性和弹性应力分别与壳剪切速率和壳应变成正比，比例系数为常数。本文所进行的分析表明，一种更通用的非线性理论可能更合适。结果表明，使用壳粘度的非线性理论可以模拟“仅压缩”行为。例如，给出了用6个周期、1.8 MHz、100 kPa声脉冲照射半径为2.03微米气泡的模拟结果。这些参数对应于de Jong等人[《超声医学与生物学》33 (2007) 653 - 656]观察到“仅压缩”行为的声学条件。还表明，使用Cross定律对壳粘度的剪切变稀行为进行建模可降低壳粘度实验估计值的方差及其对初始气泡半径 的依赖性。
