Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles.
Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles.
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DOI：
10.1016/j.ultras.2008.09.007
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发表时间：
2009-02
期刊：
影响因子：
4.2
通讯作者：
Dayton, Paul A.
中科院分区：
文献类型：
--
作者：
Doinikov, Alexander A.;Haac, Jillian F.;Dayton, Paul A.
提出了建立造影剂微泡零厚度封装模型的一般理论方法。该方法描述了一种程序，允许人们将可用的流变定律从体形式重新转换为表面形式，用于修改的Rayleigh-Plesset方程，该方程用于控制对比微泡的径向动力学。利用所提出的方法，可以对不同的包封流变规律进行测试。讨论了现有的脂包微泡壳模型所面临的挑战，如壳参数对初始气泡半径的依赖和“仅压缩”行为。利用半径在1.2 ~ 2.5 μm范围内的脂包微泡的实验半径-时间曲线分析了脂包微泡的流变行为。用20周期、3.0 MHz、100 kPa的声脉冲对磷脂包被造影剂进行超声检测，获得了实验曲线。将壳作为粘弹性固体的模型拟合实验数据，得到在上述气泡半径范围内，壳表面粘度从0.30×10-8 kg/s增加到2.63×10-8 kg/s。壳体表面弹性模量由0.054 N/m增加到0.37 N/m。提出这种增加可能是由于脂质涂层同时具有剪切减薄和应变软化材料的特性。我们假设这些复杂的流变特性不允许现有的壳模型令人满意地描述脂质包封的动力学。在现有的壳模型中，粘性壳项和弹性壳项均为线性形式，即假设作用于脂质壳内的粘性应力和弹性应力分别与壳剪切速率和壳应变成正比，且比例系数为常数。本文的分析表明，一个更一般的非线性理论可能更合适。结果表明，利用壳黏度的非线性理论可以模拟“纯压缩”行为。以半径为2.03 μm的气泡为例，给出了6周、1.8 MHz、100 kPa的声脉冲失谐的仿真结果。这些参数与de Jong等人观察到的“仅压缩”行为的声学条件相对应[超声医学生物学杂志33(2007)653-656]。研究还表明，利用Cross定律对壳黏度剪切减薄行为进行建模，可以减小壳黏度实验估计值的方差及其与初始气泡半径的依赖关系。
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.
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