A numerical study on the sub- and ultraharmonic response of an oscillating microbubble in a rigid tube

Abstract

Recently, various research within ultrasound is done on the applications of sub- and ultraharmonics responses from microbubbles, for the use in therapeutic high-intensity focused ultrasound (HIFU) and diagnostic ultrasound. Even tough some results are promising, often these experiments are done in in vitro experiments that are not comparable to in vivo situations, or the in vivo data is compared to models that do not account for damping due to the capillary wall surrounding the oscillating microbubble (e.g the solution of the Rayleigh-Plesset equation in free water). In this thesis we investigated a model that includes the influence of a restricted oscillation in a capillary tube, and compared qualitatively the sub- and ultraharmonic response from this model to the solution of the Rayleigh-Plesset equation in free-water. In addition to this, we investigated the impact of the viscosity on the free-water oscillation of the microbubbles and the sub- and ultraharmonic responses. We found that that for high viscosities the sub- and ultraharmonic responses get highly dampened and eventually disappear. The treshold for full suppresion was thereby predicted by theory for a viscosity of 1.3 mPas for ultraharmonics and above 2.2 mPas for the subharmonic. Also, we found that the responses shift to smaller microbubble sizes when a tube is added around the oscillating microbubble.