Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of a cluster of encapsulated microbubbles under the action of an ultrasound field are complex and highly nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. In this paper, based on Qin-Ferrara’s model (Qin and Ferrara, 2010), the complete synchronization and cluster formation in targeted microbubbles network are studied. Also, association schemes as a novel approach are suggested for finding a relationship between coupled microbubbles elements which are immersed in blood or surrounding soft tissue. A significant advantage of this method is that the stability of the synchronized state (or symmetric eigenmode of mutual bubble oscillation) with respect to another state (another eigenmode) can now predict. More interestingly, we find a significant relationship between an isolated and multiple microbubbles. The results show that the problem of studying the dynamics of encapsulated microbubble cluster at synchronization state is dependent on the dynamical characteristics of isolated cases, shell thickness, density. Also, the distance between microbubbles has an important role in their synchronous modes.

超声造影剂最近已在治疗实施中用于药物物质的靶向递送。在超声场的作用下，一簇封装的微气泡的径向脉动是复杂且高度非线性的，特别是对于具有高声压幅度的药物和基因传递应用而言。本文基于Qin-Ferrara模型（Qin和Ferrara，2010），研究了目标微泡网络中的完全同步和簇形成。此外，建议使用关联方案作为一种新颖的方法，以找到浸入血液或周围软组织中的耦合微泡元件之间的关系。该方法的显着优点是，现在可以预测出同步状态（或相互气泡振荡的对称本征模）相对于另一种状态（另一本征模）的稳定性。更有趣的是，我们发现一个孤立的微气泡与多个微气泡之间存在显着的关系。结果表明，在同步状态下研究微囊泡团簇动力学的问题取决于孤立情况的动力学特征，壳的厚度，密度。同样，微泡之间的距离在它们的同步模式中也起着重要的作用。结果表明，在同步状态下研究微囊泡团簇动力学的问题取决于孤立情况的动力学特征，壳的厚度，密度。同样，微泡之间的距离在其同步模式中也起着重要作用。结果表明，在同步状态下研究微囊泡团簇动力学的问题取决于孤立情况的动力学特征，壳的厚度，密度。同样，微泡之间的距离在其同步模式中也起着重要作用。