Towards a digital vascular system

Numerical simulation of blood flows has enjoyed considerable growth since the late 1990s. The most recent developments, in particular the assimilation of data into multi-physics models, have led to applications in surgical planning, improved diagnostics, medical device testing and more. In this talk, we'll show just a few examples. We will also try to show that these problems are a stimulating source of applied mathematical questions. Indeed, in parallel with advances in medical imaging and increasing computer power, recent advances in "numerical mathematics" are making increasingly realistic and efficient simulations possible. We will give an overview of some of these advances and present some open questions.