Numerous systems, from biomedical ultrasound to microfluidics, depend on the dynamic response of bubbles whose expansion is constrained by a surrounding tube or channel. For example, potential therapeutic uses of biomedical ultrasound, including localized drug delivery and clot dissolution, may be enhanced by the acoustic excitation of targeted bubbles within the blood stream. The goal of this project is to develop an understanding of the complex dynamic interactions between a gas cavity in a liquid and a surrounding compliant solid tube or channel. The physical system is quite complex because 1) it is a three-phase system, 2) the deformations of the bubble and tube can be large, and 3) the behavior of the system can be highly nonlinear. A major objective is to identify the important physical parameters and response characteristics of a constrained acoustically excited bubble. In particular, the effect of tube/channel parameters on both the resonance frequencies and nonlinear dynamic responses of bubbles (excited by a range of acoustic sources) will be characterized. To model the highly nonlinear interaction of this three-phase system with large deformations and rapidly changing time scales, simulation techniques will be developed using coupled boundary element and finite element methods. The simulation models will be updated based on the additional insight obtained from ultrasonic displacement measurements and high-speed photography observations of the responses of bubbles subject to a range of acoustic sources. A fundamental understanding of the dynamic response of bubbles to ultrasonic waves confined by vessels or channels will aid the development of a wide variety of systems including a) novel microfluidic devices, b) more effective drug delivery and activation techniques, c) new ultrasonic clot dissolution techniques, and d) guidelines for the safe use of echo contrast agents for improved diagnostic ultrasonic imaging. In addition, a Dynamic Measurements Laboratory will be developed to train undergraduate and graduate students in dynamic system response using experimental techniques such as ultrasonic displacement measurements and high-speed photography. These dynamic measurement techniques will be integrated into undergraduate and graduate laboratories and vibration classes to provide hands-on training tools. Instructional demonstrations to introduce girls in middle and high school to science and engineering will be developed using the high-speed camera.
for Grant Number: CMMI-0652947 The goal of this NSF-funded project was to develop an understanding of the complex dynamic interactions between bubbles in a liquid located within a surrounding compliant tube or channel. The original motivation of the project was to investigate potential bioeffects caused by acoustically excited echo contrast agents, which are essentially stabilized gas bubbles that can be injected into the vasculature during diagnostic or therapeutic ultrasound procedures. Intellectual Merit A variety of analytical, experimental, and numerical models were developed to study bubble and tube dynamics and predict the resonance frequencies of bubble-tube systems. Energy methods were used to develop simple analytical models that can be used to understand the fundamental characteristics of systems consisting of any number of bubbles within a compliant tube. A schematic of the model for a system with two bubbles is shown in Figure 1. The results from a 5-degree-of-freedom model, shown in Figure 2, predict four non-zero frequencies accounting for two in- and two out-of-phase oscillations for two bubbles in a compliant tube. A spherical gas body inside a gel has been developed as a reproducible experimental model of a bubble that can be easily positioned within a tube or channel. In addition, fluid-solid interaction finite element models were developed to investigate the natural frequencies of systems with a number of bubbles and variety of tube geometries. Natural frequency predictions from the simple lumped parameter model agree well with experimental measurements and finite element model simulations. A coupled finite element – boundary element code was developed to simulate the highly nonlinear interaction of axisymmetric three-phase systems with large deformations and diverse time scales. This code allows a more accurate investigation of the complex dynamic interactions between acoustically excited bubbles and a surrounding compliant solid tube or channel than previously available. Broader Impact Accurate prediction of the dynamic response of acoustically excited bubbles inside a compliant vessel or channel can aid the development of a wide variety of systems including a) novel microfluidic devices, b) more effective ultrasonic drug delivery and activation techniques, c) new ultrasonic clot dissolution techniques, and d) more informed guidelines for the safe use of echo contrast agents for improved diagnostic ultrasonic imaging. Clinical techniques are being developed and used to enhance diagnostic ultrasonic imaging by injecting stabilized gas bodies of a few microns in diameter, into the vasculature. These stabilized bubbles are called echo contrast agents because they reflect ultrasonic waves and therefore appear as bright regions in an ultrasonic image. Targeted microbubbles can be designed to adhere to tissues of interest so these regions can be more easily identified in ultrasonic images. The nonlinear coupled finite element and boundary element code can be used to predict vessel wall stresses induced by acoustically excited bubbles and identify ultrasound pressure amplitude and frequency combinations that could potentially produce bioeffects. In addition to diagnostic applications, therapeutic applications for microbubbles have been proposed, such as vehicles for drug or gene delivery or for ultrasound molecular imaging. Targeted microbubbles can be excited by ultrasonic waves so the bubbles will deliver drugs locally to the desired organ, tissue, or tumor. Energy transfer to a microbubble is increased as the ultrasonic excitation frequency approaches the bubble’s resonance frequency. Therefore, an understanding of the effects of a surrounding capillary or nearby bubbles on the bubbles’ natural frequencies can be used to optimize therapeutic applications of ultrasonically excited echo contrast agents.
