Theoretical modelling of the collapse of a shelled ultrasound contrast agent used in the treatment of cancer

Student thesis: Doctoral Thesis


Premanufactured shelled microbubbles composed of a protein shell are currently licensed in the UK as ultrasound imaging contrast agents. Current research is focussing on using the shelled microbubbles as transportation mechanisms for localised drug delivery particularly in the treatment of various types of cancer. The aim of this PhD study is to identify how the shell's material parameters influence the collapse and relaxation times of the shelled microbubbles. A theoretical model is proposed which utilises an analytical approach to predict the dynamics of a stressed, compressible shelled microbubble. This model can be used to identify the optimal material parameters for the shells. A neo-Hookean, compressible strain energy density function is used to model the potential energy per unit volume of the shell. A stress is applied to the inner surface of the spherical shell whilst setting the outer surface's stress to zero. The collapse phase of the stressed shelled microbubble is then considered. Applying the momentum balance law,a dynamical model is used to predict the dynamics of the collapsing shelled microbubble. An analytical approach is adopted using an asymptotic expansion. A second model is then constructed to model the deformation of an open, shelled microbubble. This is achieved by considering a reference configuration (stress free)consisting of a shelled microbubble with a spherical cap removed. This is then deformed angularly and radially by applying a stress load to the free edge of the shell. This forms a deformed open sphere possessing a stress. This is used to represent the change in geometry of a shelled microbubble. The third and final model focusses on developing a Rayleigh-Plesset equation for an incompressible,thin shelled, gas loaded shelled microbubble with a shell that is composed of a liquid-crystalline material. The technique of linearisation is used to predict the shelled microbubble's natural frequency and relaxation time. The influence of the material properties of the shell on the natural frequency and relaxation time are discussed.
Date of Award22 Jun 2017
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council)

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