Theoretical investigation of shear stress generated by a contrast microbubble on the cell membrane as a mechanism for sonoporation

There are numerous experimental investigations on sonoporation, while the theoretical background of this phenomenon still is in its infancy. One of the suggested mechanisms of sonoporation is linked to shear stress exerted on the cell membrane by acoustic microstreaming generated by a contrast microbubble pulsating nearby a cell. Currently, the existing model of this effect is based on an equation that has been derived for a free hemispherical bubble resting on a rigid plane. Such a model is not adequate for a contrast microbubble. In this paper, an improved theory is suggested that assumes an encapsulated bubble to be detached from the cell membrane. The improved model allows one to calculate the shear stress distribution on the cell membrane at different values of the acoustic parameters. The second problem considered is how to apply the model for pairwise bubble-cell interactions to bubble-cell solutions, which one has to deal with in experiments. An approach is proposed to evaluate the number of sonoporated cells in a bubble-cell solution. It is shown that the reaction of a bubble-cell solution to the variation of the acoustic parameters can be different from what is predicted by the analysis of interactions between single bubbles and cells.