Sarah McBurnie - Medical ultrasound – injecting mathematics into the problem of “bubbly blood”

Ultrasound, which is sound above human hearing, is used in medicine to image the interior of the body. The process used is similar to that used by dolphins and bats; sound is fired at the target area we want to “see” and the echoes returned are interpreted so that we can map out the boundaries between different anatomical structures in that area.

In some types of diagnostic imaging, tiny bubbles are injected into the blood to improve the backscatter (or echo) from blood tissue in a way that enhances and improves the ultrasonic scan image. However, ultrasound propagation through the bubble clouds is not yet fully understood. Consequently, incorrect displays of anatomy can occur in the image, and these are known as artifacts. If an improved model for the acoustic scattering can be derived, then the image generated could be further improved and corrections made for artifacts.

Inspired by this medical application, we use homogenization techniques to derive averaged equations for the pressure induced on bubbly liquids by a sound wave.

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