| Microbubbles are used as contrast agents in diagnostic ultrasound, and as transport agents or to engender physical effects in therapeutic ultrasound. The distinguishing characteristic of bubbles is their small size, on the order of microns, which allows them to traverse the smallest capillaries in the human body. Furthermore, when subject to acoustic forcing (ultrasound), the oscillations of bubbles become highly nonlinear, leading to a unique echo characteristic. Bubble echo improves the clinician's ability to distinguish between blood carrying contrast agent from the surrounding tissue. Present ultrasound techniques, however, do not take full advantage of the nonlinear properties of oscillating microbubbles. In this work, a novel method to maximize the bubble echo, thereby improving image quality, is suggested. Pulse-inversion imaging is utilized as a means of filtering out the linear echo of surrounding tissue. A norm is defined for the nonlinear bubble echo and it is shown how the norm may be maximized, given a limit on ultrasound intensity, by optimizing the acoustic pulse shape using optimal control theory. The optimization is performed for a single bubble of a particular size. The optimal pulse yields a several-fold increase in the echo norm over conventional pulse driving. It is also shown that the optimal pulse effectively maximizes the echo of a bubble cloud with mean size equal to that of the single bubble. Increased bubble response comes as a result of severe radial collapse, which in turn drives the translation dynamics of the bubble. These motions have been observed by others in experiment, but have, up this point, been inadequately explained. The erratic translation of a bubble is found to be intimately coupled to the radial dynamics, especially in the case of violent oscillations. The assumption of spherical symmetry is relaxed and it is considered how bubble translation can be a mechanism for shape instability, thereby leading to bubble destruction and more rapid dissolution. Unexpectedly, however, cases are discovered where violent bubble collapse appears to have a stabilizing effect on shape oscillations. Finally, future avenues are suggested in clinical devices and practice in which the present work could be developed. |
