Coupled Radial and Translational Responses of Microbubbles Subject to Ultrasound Driving Within a Biomedical Framework

Microbubbles interacting with acoustic waves are at the foundation of both diagnostic and therapeutic medical techniques. The focus of this work is set on two particular classes of applications: pulsating microbubbles as contrast agents in medical imaging; and cavitating microbubbles in kidney stone comminution protocols. Microbubble contrast agents injected in the bloodstream scatter the incoming acoustic waves originating from a transducer differently than the surrounding tissue and as such, can be used for medical imaging purposes. Because the magnitude of the acoustic radiation force can be significant, the hydrodynamic behavior of those bubbles may be modified during ultrasound measurements: as a consequence, the information extracted may be biased. Because displacement is intrinsically linked to linear momentum, the two equations describing the radial and translational motions are coupled. We first examine two translation approximating schemes, both based on the assumption of weak acoustic forcing. Solution of the equation of motion for linearly oscillating bubbles shows that even for weak acoustic forcing, the approximation of the translation velocity departs sometimes significantly from its fully-resolved counterpart. The error depends on the bubble size, the driving frequency, and the liquid properties. In a second part, an improved approximation is formulated, which allows one to understand better the dynamic fundamentals of bubble translation, including transient scaling and key driving forces. From the information provided by these approximations, we suggest new ways to predict some of the effects of the acoustic radiation force in applications such as targeted drug delivery, selective bubble driving and accumulation. Building upon these results, we then expand the scope of this dissertation in Chapter 5 to the related subject of microbubble management in microgravity. Similarly, it has been observed that small and stable bubbles can accumulate in microfluidic devices and may in some cases disrupt normal flowing conditions. To address these problems, we determine an optimal acoustic waveform aimed at maximizing bubble displacement over one period. To do so, we use radial variance as the basic cost function of an optimal control problem, along with other constraints. The efficacy of the optimally modified acoustic waveform is examined across the driving frequency spectrum and is found to be a significant improvement over regular sine waves of similar intensities and frequency. Finally, we follow up on a previous investigation about the collateral damage caused by inertially expanding microbubbles during shockwave lithotripsy (SWL). The latter process is used extensively in urology to treat kidney stone. There, a series of strong lithotripter shockwaves (LSW) is focussed on the kidney region so as to fragment the stone. While there exists other key mechanisms in addition to those directly related to microbubbles, cavitating and later imploding gas bubbles in the vicinity of the stone were shown to participate in the stone comminution. These processes are likely to compromise the integrity of nearby tissue (e.g., capillary rupture). In this dissertation, we investigate two bubble-bubble mechanisms that may modify bubble behavior and in turn, affect the maximum size achievable by a bubble subject to a LSW. Namely, we analyze the effect of time delays on the cavitation growth of microbubbles and use a set of coalescing bubble equations which incorporate the presence of water vapor in the strongly expanding bubbles.