超声波场中造影剂包膜气泡的界面稳定性研究

Encapsulated bubbles are widely used in medical ultrasound applications, e.g. ultrasound perfusion imaging. The stability of the encapsulating membrane exposed in an ultrasound field is of importance in the ultrasound contrast agents. The deformation induced by the ultrasonic pressure wave may lead to the break-up of a bubble, and thereby shorten the residence time of contrast agents. Most of the existing studies on the stability of the encapsulated bubble were confined to the single-bubble model, while the previous studies on the stability of the bubbles mainly focused on gas bubbles without encapsulating membranes. The objective of this study is to establish an analytical model of the stabilities of multi-bubbles encapsulated with viscoelastic membranes under the viscous and compressible ultrasound field. In the theoretical study, we will utilize the homogenization methods to investigate the nonlinear resonance relationship among the zeroth-order (the radial motion), the first-order (the translation motion) and the higher-order (the shape deformation) oscillations, and their resonance interactions with the driving ultrasound, respectively. Accordingly, we will obtain the conditions under which the surface of the encapsulated bubbles would become unstable. The parameters of the ultrasound, such as the frequency and amplitude, and the encapsulating membrane, such as the moduli of elasticity and bending, are of our interest. In the numerical study, we will adopt the immersed boundary methods to capture the shapes of the bubbles precisely. The ultrasound field is represented by the flow field with pressure waves, compressibility and viscosity. We will simulate the coupling developments of different shape modes subjected to the ultrasonic pressure wave. In this way, we can investigate the nonlinear transformation among different oscillatory modes. The influences of the translations and shape oscillations of the surrounding bubbles, the effects of the blood vessels, and the role of the viscous boundary layer out of the encapsulated bubble interface on the stability of membrane will be discussed. The theoretical analysis and numerical simulation will become auxiliary means for improving the quality of imaging through controlling the parameters of encapsulating membranes and ultrasound. The study of the stability of encapsulted bubbles will provide instruction in the preparation of ultrasound contrast agents and the improvement of ultrasound perfusion imaging technique.

造影剂包膜气泡的界面稳定性是决定超声灌注成像质量的关键。目前对包膜气泡稳定性的研究多局限于单个气泡模型，而对气泡群的稳定性研究多局限于一般的无包膜气泡。本研究拟建立多个粘弹性包膜气泡与超声波粘性可压缩流场相耦合的稳定性分析平台。运用多时间尺度的理论分析方法，研究零阶（径向振动）、一阶（平移运动）和高阶（形状振动）各阶模态之间的非线性共振关系，结合外加超声波的频率、强度、波形等参数，得出包膜气泡界面不稳定产生的条件。运用基于浸入边界法的流固耦合数值模拟程序实现对包膜气泡界面的捕捉，模拟真实超声波场中气泡各阶模态的非线性发展过程，讨论气泡群中周围气泡的相对平移运动、形状振动及血管壁的受限环境对界面稳定性的干扰作用，分析流场粘性对稳定性的影响。本项目为通过控制包膜和超声波的物理参数以提高成像效率的方法提供科学依据，对超声造影剂的制备和超声灌注成像技术的完善具有指导意义。

造影剂包膜气泡的界面稳定性是决定超声灌注成像质量的关键。本项目建立超声造影剂包膜气泡在超声波流场中的界面稳定性分析平台。基于水动力和粘弹性应力相耦合的力学模型，建立包膜气泡在粘性流场中的动力学方程，推导出各阶模态共振频率的数学表达式，明确粘性对共振频率的重要影响，得到零阶（径向振动）、一阶（平移运动）和高阶（形状振动）各阶模态之间的共振关系和发生界面不稳定的条件，并通过膜的应力特征判断气泡界面易于破裂的薄弱点。研究超声波的频率、波形、强度等参数对包膜气泡界面稳定性的影响，发现在超声波的双频激励下，造影剂气泡可产生更丰富的高阶谐振，并且更有助于维持气泡界面的稳定性，分析其原因在于双频激励在基频上激发的散射强度明显低于单频激励，由此可认为双频激励较之单频激励在提高超声成像的质量和延长超声造影时间上更具优势。建立双包膜气泡的动力学模型，模型通过了实验和经典Bjerknes理论的验证，模型可有效分析出包膜气泡在相互作用过程中的平移运动特征、阻力特征和界面形变特征。本项目的研究为有针对性的调节包膜的弹性、粘性等参数和超声波的频率、波形、强度等参数，提高超声成像效率提供科学依据。

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