Eulerian finite element method for the numerical modeling of fluid dynamics of natural and pathological aortic valves

What is it about?

We present a finite element methodology tailored for the simulation of pulsatile flow in the full aorta and sinus of Valsalva interacting with highly deformable thin leaflets. We describe an extension of the so-called “Resistive Immersed Surface” method. To circumvent stability issues resulting from the bad conditioning of the linear system, especially when flow and geometry become complex after the inclusion of the aorta, we use a Lagrange multiplier technique that couples the dynamics of valve and flow. A banded level set variant allows to address the singularity of the resulting linear system while featuring, in addition to the parallel implementation, higher accuracy and an affordable computational burden. High-fidelity computational geometries are built and simulations are performed under physiological conditions. Several numerical experiments illustrate the ability of the model to capture the basic fluidic phenomena in both healthy and pathological configurations. We finally examine numerically the flow dynamics in the sinus of Valsalva after Transcatheter Aortic Valve Implantation. We show numerically that flow may be subject to stagnation in the lower part of the sinuses. We highlight the far-reaching implications of this phenomenon and we hope inciting adequate studies to further investigate its potential clinical consequences.

Featured Image

Photo by Ali Hajiluyi on Unsplash

Photo by Ali Hajiluyi on Unsplash

Why is it important?

• Hemodynamics in full aorta and aortic sinuses coupled with highly deformable valve. • An exact Lagrange multiplier technique couples the dynamics of valve and flow. • A damped-Newton strategy allows more stability for relatively large Reynolds numbers. • Numerical examples in 2D and 3D with healthy and pathological valves. • Numerical investigations pinpoint a risk of blood stagnation after Transcatheter Aortic Valve Implantation.