The Influence of Compressibility on the Dynamics of Encapsulated Microbubbles
Please note that this project is self-funded.
The dynamics of EMBs in viscoelastic fluids forced by ultrasound forms the focus of this project.
Thin-shell encapsulated microbubbles (EMBs) are gas-filled microbubbles encased in a stiff albumin or flexible lipid shell. They have been shown to improve the performance of biomedical procedures such as ultrasound contrast imaging, targeted drug delivery and sonoporation.
The viscoelastic fluid will be modelled using models such as the Oldroyd B model while the properties of the shell are accounted for through the dynamic boundary condition at the bubble surface.
An interdisciplinary approach combining models for cell mechanics with bubble dynamics will provide insights into the deformation of cellular entities subject to cavitation flow and to enhance drug delivery via coated microbubbles. Ultrasonic cavitation is one of the most effective cleaning agents. For example, it is used to clean and to disinfect surgical instruments in hospitals. There is a wide range of other biomedical applications that will benefit from the computational models developed in this project.
Project aims and methods
A boundary integral method (BIM) will be developed for this problem. This will be validated against a simple model for spherical oscillations of a coated bubble (Rayleigh-Plesset equation). A three-dimensional model of ultrasound contrast agents (UCAs) subject to high intensity ultrasound will be developed based on the BIM. The effects of a thin encapsulating shell are approximated by modifying Hoff’s model for encapsulated spherical bubbles to the nonspherical case. The generation of a high-quality mesh for the fully 3D problem is crucial and this aspect of the numerical method will be explored in depth.
Comparisons with experimental results will be made where available ensuring that fluid parameters are chosen using available data from material characterisation.
You will learn about different methods for discretising partial differential equations and iterative methods for solving the resulting systems of algebraic equations. You will also develop an understanding about the theoretical properties of partial differential equations. There will also be an element of scientific computing and the student will develop programming skills using MATLAB, C++ etc.
For programme structure, entry requirements and how to apply, visit the Mathematics programme.View programme