  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 [S.P. Qin, K.W. Ferrara, J. Acoust. Soc.
Am. 128 (2010) 1511], 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.
