Finite element modelling of phospholipid-shelled microbubbles for therapeutic uses at low acoustic pressures

The use of clinical Ultrasound Contrast Agents (UCAs), in the recent years, has seen novel applications, such as the development of UCAs for therapeutic drug delivery for the treatment of cancerous tumours and gene therapy. Common UCAs are microbubbles encapsulated with a monolayer of amphiphilic molecules, such as phospholipids or fatty acids. The interaction of the molecules at the interface with the adjacent gas and liquid phases in the presence of an acoustic pressure allows the occurrence of bending moments and shear forces in the coating, which emerge as surface waves. In this study, the surface modes of SonoVue microbubbles are observed using high-speed imaging, and accordingly are compared to the numerical solutions of a three-dimensional finite element model. Comsol Multiphysics is employed in an effort to implement the viscoelastic properties of the thin material encapsulating SonoVue UCA. This work discusses the possible problems encountered in finite element analysis to model the deformation of thin viscoelastic shells. The proposed model allows the simulation of non-spherical deformations at low acoustic pressures (50-80 kPa) in an effort to examine the mechanisms contributing to the presence of shell modes. The numerical results demonstrate that the surface mode amplitudes are dependent on a relaxation time, which models the time necessary for the amphiphilic molecules to reach an equilibrium state. Additionally, a decrease of separation distance between a microbubble and a thin viscoelastic membrane is shown as contributing to the doubling of the surface mode amplitude. The finite element model is able to show that significant perturbation in a cell membrane is present when a bubble exhibited surface modes of the second order. These effects are shown to contribute to the understanding of the effectiveness of sonoporation - a process during which cell membranes show an increase of permeability in the presence of ultrasound and UCAs, thus permitting therapeutic agents to enter the cells.