Cardiovascular Fluid Structure Interaction

Mathematical models of the mechanical properties of the cardiovascular system play an increasingly important role in the diagnostics and treatment of cardiovascular disease and, in addition, can provide valuable information to pathological studies aiming to understand the genesis of cardiovascular disorders like atherosclerosis, heart failure and heart valve deficiency.
Biomechanics of the cardiovascular system is characterized by the interaction of blood flow with surrounding structures, like the vessel wall and the heart muscle, and immersed structures like heart valves and medical devices. In the presentation, several aspects of this fluid structure interaction, and especially the complexity of the structures involved, will be addressed. Examples of the use of arbitrary Euler-Lagrange methods for the flow in the left ventricle and fictitious domain methods for heart valve dynamics will be given.
Depending on the kind of analysis to be performed and the detail in information that is needed, three distinct approaches (lumped-parameter models, 1D wave propagation models, and fully 3D fluid-solid interaction
models) can be used to model the mechanics of the cardiovascular system.
Examples of a simple heart muscle contraction model, an arterial wave propagation model and a fully 3D model of the flow in geometrically complex arteries will be presented to elucidate the difference and the relation between the three approaches.