Study of encapsulated microbubble cluster based on association schemes perspective.

Highlights • The dynamical behaviors of N -interacting microbubble cluster is investigated in framework of association schemes theory and Bose-Mesner algebra. • Where the complete synchronization and cluster formation in targeted microbubbles network are studied. • The distances between interacting UCAs cluster have mainly role in their synchronization states. • By introduced direct product of two different schemes, we can have an extension of interacting targeted microbubbles to network motifs from smaller ones. Abstract 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. [ABSTRACT FROM AUTHOR]