On the theory of multiple encapsulated microbubbles interaction: Effect of lipid shell thickness

Abstract

Encapsulated microbubbles are empty, micrometer-sized, spherical bubbles, typically micron which are used in many applications as lipid-shells in soft tissues. Here, this paper proposes the theoretical and mathematical modelling of the interaction of lipid-encapsulated microbubbles in soft tissues, as well as an examination of the effect of the thickness of the lipid-encapsulated microbubbles envelope located between the inner and outer radius of the microbubble. The mathematical models are formulated for a single encapsulated microbubble and interacting microbubbles in lipid shells. The first models are placed while considering the effect of shell-thickness on microbubbles in soft tissues. The second one has weak shell-thickness layers on it. In encapsulated single microbubbles and interacting microbubbles, the modified Church equations of shell-thickness microbubbles are formulated and solved analytically. Under the effect of layer thickness, the radii of outer microbubble dynamics are larger than those of inner radii of encapsulated microbubble dynamics, and the radii of bubbles with weak shell thickness in soft tissue are smaller. The clusterization of microbubbles reduces the process of microbubble growth, and interparticle interaction enhances it. In addition, the approximate value of the inner and outer microbubble radius was calculated at the different time intervals when the thickness of the shell, δ=0,15,150,250,350nm. Moreover, the growth process has been studied in different materials such as polymers, albumin, lipids, and liquids, and it turns out the results are consistent with previous works.