A mathematical model of sonoporation using a liquid-crystalline shelled microbubble

In recent years there has been a great deal of interest in using thin shelled microbubbles as a transportation mechanism for localised drug delivery, particularly for the treatment of various types of cancer. The technique used for such site-specific drug delivery is sonoporation. Despite there being numerous experimental studies on sonoporation, the mathematical modelling of this technique has still not been extensively researched. Presently there exists a very small body of work that models both hemispherical and spherical shelled microbubbles sonoporating due to acoustic microstreaming. Acoustic microstreaming is believed to be the dominant mechanism for sonoporation via shelled microbubbles. Rather than considering the shell of the microbubble to be composed of a thin protein, which is typical in the literature, in this paper we consider the shell to be a liquid-crystalline material. Up until now there have been no studies reported in the literature pertaining to sonoporation of a liquid-crystalline shelled microbubble. A mathematical expression is derived for the maximum wall shear stress, illustrating its dependency on the shell's various material parameters. A sensitivity analysis is performed for the wall shear stress considering the shell's thickness; its local density; the elastic constant of the liquid-crystalline material; the interfacial surface tension and; the shell's viscoelastic properties. In some cases, our results indicate that a liquid-crystalline shelled microbubble may yield a maximum wall shear stress that is two orders of magnitude greater than the stress generated by commercial shelled microbubbles that are currently in use within the scientific community. In conclusion, our preliminary analysis suggests that using liquid-crystalline shelled microbubbles may significantly enhance the efficiency of site-specific drug delivery.