Computational Fluid Dynamics Characterization of Blood Flow in Central Aorta to Pulmonary Artery Connections: Importance of Shunt Angulation as a Determinant of Shear Stress-Induced Thrombosis

Abstract

The central aortic shunt, consisting of a Gore-Tex (polytetrafluoroethylene) tube (graft) connecting the ascending aorta to the pulmonary artery, is a palliative operation for neonates with cyanotic congenital heart disease. These tubes often have an extended length, and therefore must be angulated to complete the connection to the posterior pulmonary arteries. Thrombosis of the graft is not uncommon and can be life-threatening. We have shown that a viscous fluid (such as blood) traversing a curve or bend in a small-caliber vessel or conduit can give rise to marked increases in wall shear stress, which is the major mechanical factor responsible for vascular thrombosis. Thus, the objective of this study was to use computational fluid dynamics to investigate whether wall shear stress (and shear rate) generated in angulated central aorta-to-pulmonary artery connections, in vivo, can be of magnitude and distribution to initiate platelet activation/aggregation, ultimately leading to thrombus formation. Anatomical features required to construct the computer-simulated blood flow pathways were verified from angiograms of central aortic shunts in patients. For the modeled central aortic shunts, we found wall shear stresses of (80–200 N/m²), with shear rates of (16,000–40,000/s), at sites of even modest curvature, to be high enough to cause platelet-mediated shunt thrombosis. The corresponding energy losses for the fluid transitions through the aorta-to-pulmonary connections constituted (70 %) of the incoming flow’s mechanical energy. The associated velocity fields within these shunts exhibited vortices, eddies, and flow stagnation/recirculation, which are thrombogenic in nature and conducive to energy dissipation. Angulation-induced, shear stress-mediated shunt thrombosis is insensitive to aspirin therapy alone. Thus, for patients with central aortic shunts of longer length and with angulation, aspirin alone will provide insufficient protection against clotting. These patients are at risk for shunt thrombosis and significant morbidity and mortality, unless their anticoagulation regimen includes additional antiplatelet medications.

Appendix

Curvature is a measure of how sharply a curve bends. Curvature is zero for a straight line, small in value for curves which bend little and large for curves which angle sharply. The equation for a symmetric parabola, restricted to the Cartesian (x,y) plane, and with vertex at the origin (0,0), has the simple form y = x ²/4f, where f (referred to as the focal length) is a constant describing the degree of curvature. The curvature (K) at a point (x) along the curve is given by K(x) = [4f ²/(4f ² + x ²)^3/2], which has its maximal value at the vertex of the parabola, i.e., at x = 0, with K(0) = 1/2f. The parabolic tubular vessels in this study were constructed by sweeping a circular cross-sectional area along a parabolic path. This path was defined as the higher curvature of the two curves obtained by intersection of the tube wall with the plane containing the entire centerline. In defining the geometry this way, the maximum curvature that may be defined, without causing the tube to intersect upon itself, is virtually unbounded. A caveat to defining the geometry in this manner is that it complicates the equation for the centerline, since a curve parallel to a parabola is, in fact, not a parabola. To maintain a total tube centerline arc length of 40 mm, for varying focal lengths, an equation describing the centerline was determined as a function of the parabolic focal length and the tube’s radius. Within the Autodesk Inventor software, a macro was written to iterate the centerline’s end points, utilizing the Newton–Rhapson method, such that a total vessel centerline length of 40 mm is maintained, for all focal lengths considered. ANSYS’ Design of Experiments feature was then used to automate: generating the desired tubular pathway, meshing the domain and numerically solving the associated fluid dynamics differential equations with FLUENT.