Waves and bubbles: The mathematics of ultrasound imaging

by Teresa Rauscher

Tuesday 10 Nov 2026, 13:00 → 14:00 Europe/Vienna

SR 11.32 (University of Graz)

How can tiny bubbles help us see inside the human body? In contrast-enhanced ultrasound imaging, microscopic gas bubbles are introduced into the bloodstream to make blood flow and vessels more visible. Sound waves make these bubbles expand and contract, while the bubbles themselves influence the surrounding sound field.

In this talk, I will explain how we can describe this interaction using mathematical equations: one for the propagation of sound and another for the motion of the bubbles. Building such a model is only the beginning: we also need to understand whether its equations have solutions and how these solutions behave. Combining mathematical ideas with illustrative simulations, I will give an introduction to my research on nonlinear waves and ultrasound contrast imaging.