| Summary: | In recent years, ultrasound and microbubble contrast agents have been shown to have potential to become very powerful diagnostic tools in medical applications, particularly in the areas of drug/gene delivery and site targeted imaging. While a fairly substantial amount of experimental research has been conducted, their behaviour is yet to be fully understood. This is paramount in increasing the reliability and effectiveness of the microbubbles while ensuring patient safety. The aim of this thesis is to investigate the effects of boundary, bubble size, bubble arrangement and cluster size on the dynamical behaviour of the cluster and to see if chaotic or bifurcation characteristics could be helpful in diagnostics. Small encapsulated microbubbles subjected to appropriate variations in ultrasound pressure amplitude were considered to mimic practical applications. It was found that under these conditions, the system becomes numerically stiff. Therefore a code based on the numerical difference formula was written to- solve the normalised Keller-Miksis-Parlitz model equation to trace-the bubble dynamics. The-resulting-oscillations were analysed-in terms of bifurcation diagrams, Poincaré plots, Floquet analysis and Fourier spectra. It was found that as monodispersed microbubbles were clustered closer together, the oscillation amplitude for a given applied ultrasound power was reduced, and for inter-bubble spacing smaller than about ten bubble radii nonlinear subharmonics and ultraharmonics were eliminated. For clustered microbubbles, as for isolated microbubbles, an increase in the applied acoustic power caused bifurcations and transition to chaos. The bifurcations preceding chaotic behaviour were identified by Floquet analysis and confirmed to be of the period-doubling type. As the number of microbubbles in a cluster increased, regularisation occurred at lower ultrasound power and more windows of order appeared. The model was also modified to account for the presence of the wall. It was shown that for a monodispersed cluster of microbubbles near a wall, the route of chaos was altered. Microbubbles that were close to a boundary exhibited an intermittent route to chaos while microbubbles that were further away from the boundary exhibited period doubling route to chaos. In additiOn, strong boundary-microbubble coupling effects caused the natural frequency of the bubble system to decrease and produced larger shifts in the chaotic threshold. By varying the arrangement, size of the microbubbles and the size of the bubble cluster, it was found that larger-sized microbubbles exhibited profound
influence on the inter bubble interaction by either changing the resulting route to chaos in a cluster of mainly smaller microbubbles, or stabilising the cluster dynamics by suppressing chaotic oscillations in a cluster of larger microbubbles. It was also found that the cluster will exhibit the same type of attractor in spite of the different microbubble sizes within the cluster and
the variation of the inter bubble distance. It is anticipated that, whenva1idatedby-experiment, the results obtained in this thesis have the potential to serve as-a- guide for the development of microbubbles in biomedical applications. This conceptual study, in conjunction with other approaches discussed in the literature, may serve the purpose of improving the diagnostic sensitivity of ultrasound targeting of medical agents and enabling more control and accuracy in medical therapeutic procedures.
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