Date: Tuesday, March 8, 2016
Time: 3:00pm – 4:00pm
Room: Blocker 506A
Speaker: Dr. Anthony J. Mulholland (University of Strathclyde)
Title: Theoretical Modelling of the Collapse of a Shelled Ultrasound Contrast Agent for use in the Treatment of Cancer
Abstract:
Premanufactured shelled microbubbles composed of a protein shell are currently licensed as ultrasound imaging contrast agents. Current research however is focussing on using the microbubbles as transportation mechanisms for localised drug delivery particularly in the treatment of various types of cancer. It is of interest therefore 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 both an analytical and a numerical approach to predict the dynamics of a stressed, compressible shelled microbubble. 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 via a series of small stresses whilst setting the outer surface’s stress to zero. The spatial profiles of the Cauchy radial and angular (hoop) stresses that are generated within the shell as a consequence of the stressing are stored during the quasistatic inflationary process (forward picture). The collapse phase of the stressed shelled microbubble is then considered. An analytical approach is adopted using an asymptotic expansion alongside a numerical scheme. Results from the model show the influence of the shell’s thickness, Poisson’s ratio and the shear modulus on the collapse times. A second model is then constructed to predict the collapse time for an unfolding shell. This is achieved by considering a reference configuration (stress free) consisting of a shelled microsphere with a hemispherical cap removed. Some comparison with recent experimental observations will be discussed.
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