# Bubble Wonder – Researchers Develop New Mathematical Model to Enhance Ultrasound Resolution

Researchers at the University of Tsukuba have developed a mathematical formula that accounts for the compressibility of encapsulated microbubbles in the propagation of ultrasonic waves, potentially improving ultrasound imaging resolution and enabling more precise drug delivery.

A team of scientists at the University of Tsukuba has created a mathematical model that describes the relationship between sound waves and multiple encapsulated microbubbles, which are commonly used as contrast agents for ultrasound. This breakthrough could potentially aid advancements in the fields of medical imaging and drug delivery.

Researchers from the University of Tsukuba have derived a novel theoretical formula that predicts the behavior of ultrasound waves as they traverse through liquids that contain encapsulated bubbles. The team discovered that factoring in the compressibility of the bubble shell was crucial in accurately forecasting the movement and interaction of these sound waves. This research could pave the way for advancements in ultrasound imaging resolution, based on the creation of more effective contrast agents.

Ultrasound has become a vital tool in modern health care because it can provide doctors with detailed diagnostic images safely and non-invasively. The technology works by sending high-frequency sound waves from a transducer and listening for the echoes created at the interface between tissues of different densities. Based on the time it takes for the echoes to return, the computer can reconstruct the image. However, one of the major drawbacks of ultrasound is its low resolution, which means that contrast agents, like microbubbles, are used for echocardiograms or liver scans. A better theoretical understanding of the physics of the interaction between encapsulated microbubbles, which possess a thick shell, and sound waves is still needed to create better contrast agents.

Now, researchers at the University of Tsukuba have derived new nonlinear equations that take into account the compressibility of the shell layer to extend its applicability to multiple bubbles. The researchers chose this path because previous work did not model realistic properties for the bubble surface. “We modeled the shell as a viscoelastic object, which turned out to be an important factor in the analysis,” author Professor Tetsuya Kanagawa says.

Compressibility measures the relative change in the volume of fluid or solid in response to an increase or decrease in pressure. Other research projects tended to focus on the deformations of the bubble’s interior while neglecting the bubble itself. The researchers found that the effect of including the shell in the calculations led to an increase in the attenuation (dissipation) coefficient.

“Our work helps pave the way for future refinements to the theory of sound attenuation in liquids,” Professor Kanagawa says. The microbubbles studied in this project might also be converted to therapeutic uses, such as targeted drug delivery. In that case, sound waves could cause the bubbles to burst at specific times or locations in the body, releasing the drug.

Reference: “Nonlinear acoustic theory on flowing liquid containing multiple microbubbles coated by a compressible visco-elastic shell: Low and high frequency cases” by Tetsuya Kanagawa, Mitsuhiro Honda and Yusei Kikuchi, 6 February 2023, Physics of Fluids.
DOI: 10.1063/5.0101219