Improved characterisation and modelling of microbubbles in biomedical applications

Interest in coated microbubbles as agents for therapeutic and quantitative imaging applications in biomedical ultrasound has increased the need for their accurate modelling. However, effects such as gas diffusion, the properties of the coating and changes in bubble behaviour under repeated ultrasound pulses are still poorly understood. The work described in this thesis attempts to develop new theoretical descriptions of microbubble behaviour to address this challenge. In the first part of the thesis, a model of gas exchange into and out of bubbles in tissue under a varying external pressure is developed and applied to the computationally simpler problem of decompression diving. It is concluded that gas diffusion can explain bubble growth and the model validates current decompression algorithms. In the second part of the thesis, a revised equation of motion for microbubble oscillation is proposed that includes the effects of gas diffusion and a time-dependent surfactant surface concentration. This is subsequently incorporated into a nonlinear wave propagation model to account for these additional effects in the response of microbubble contrast agents to ultrasound excitation. Furthermore, the accuracy of a recently proposed computationally efficient method of modelling nonlinear propagation through a polydisperse bubble population is investigated. However, the approximation is concluded to be insufficiently accurate for parameter regimes corresponding to biomedical ultrasound. The results from the new model for microbubble dynamics indicate significant changes in both bubble behaviour and the character of the propagated pulse, demonstrating better agreement with experimental data than predictions from existing models. The results strongly suggest that changes in bubble dynamics are dominated both by surfactant shedding on ultrasonic timescales and gas diffusion over longer timescales between pulses. Incorporating such time-dependent phenomena in ultrasound imaging algorithms should lead to better quantitative agreement with experiment and guide future improvements in the clinical implementation of microbubble contrast agents

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