Fluid Mechanics of Deformable Aortic Prostheses

The simultaneous replacement of a diseased aortic valve, aortic root and ascending aorta with a composite graft equipped with a prosthetic valve is a nowadays standard surgical approach in which the Valsalva sinuses of the aortic root are sacrificed and the coronary arteries are reconnected directly to the graft (Bentall procedure). In practice, two different polyethylene terephthalate (Dacron) prostheses are largely used by surgeons: a standard straight graft and a graft with a bulged portion that better reproduces the aortic root anatomy (Valsalva graft). The aim of the present investigation is to study the effect of the graft geometry, with its pseudo-sinuses, on the the flowfield, with particular attention to the coronary entry-flow, and on the stress concentration at the level of coronary-root anastomoses during the cardiac cycle. A bi-leaflet mechanical valve with curved leaflets is considered, attached to the two different prostheses. Two cylindrical channels, reproducing the very early coronary vasculature are connected to the grafts. An accurate three-dimensional numerical method, based on the immersed boundary technique, is proposed to study the flow inside deformable geometries. Direct numerical simulations of the flow inside the prostheses under physiological pulsatile inflow conditions are presented. The dynamics of the leaflets (considered rigid) is obtained by a fully-coupled fluid-structure-interaction approach, while a weak-coupled approach is employed for the deforming roots, in order to reduce the computational cost, using optimized solvers for both the fluid and structural problems. The Dacron material is modeled as orthotropic, with an inversion of the material properties in longitudinal and circumferential direction for the skirt region of the Valsalva prosthesis. Coronary perfusion is reproduced modulating in time the porosity, and thus the resistance, of the coronary channels. The results indicate that while the pseudo-sinuses do not significantly influence the coronary entry-flow, their presence allows for smaller levels of stresses at the level of coronary-root anastomoses, potentially reducing post-operative complications.