A vein for applied mathematics
Numerical simulation in the field of tension between mathematics, mechanics and medicine

Atherosclerosis is a common systemic disease of the arterial wall. The resulting plaques can lead to reduced blood flow due to vasoconstriction, but also to thrombosis due to rupture. In this context, the calculation of arterial wall stresses is of particular interest. Based on patient-specific intravascular ultrasound (IVUS) data, the geometry of arteries can be mapped in the computer and nonlinear elasticity models from mechanics can be used to model the wall stresses. Besides the nonlinearity of the structural models, the anisotropy and the incompressibility of the tissue pose a challenge for the numerical simulation and the underlying mathematical algorithms. The discretization by finite elements leads to systems with several million unknowns which can only be solved by parallel scalable algorithms on powerful parallel computers. A central task of numerical mathematics is to develop reliable and powerful algorithms for this problem. In the lecture the different aspects, starting from the IVUS data up to the stress calculation, presented from the numerical point of view. Another challenge is the deformation of the arterial wall, taking into account the blood flow. In the lecture new results for the simulation of the coupled fluid-structure interaction of arteries and blood flow with special consideration of nonlinear arterial wall models will be presented.