Numerical Simulation of Wall Shear Stress Conditions and Platelet Localization in Realistic End-to-Side Arterial Anastomoses

Abstract

Research studies over the last three decades have established that hemodynamic interactions with the vascular surface as well as surgical injury are inciting mechanisms capable of eliciting distal anastomotic intimal hyperplasia (IH) and ultimate bypass graft failure. While abnormal wall shear stress (WSS) conditions have been widely shown to affect vascular biology and arterial wall self-regulation, the near-wall localization of critical blood particles by convection and diffusion may also play a significant role in IH development. It is hypothesized that locations of elevated platelet interactions with reactive or activated vascular surfaces, due to injury or endothelial dysfunction, are highly susceptible to IH initialization and progression. In an effort to assess the potential role of platelet-wall interactions, experimentally validated particle-hemodynamic simulations have been conducted for two commonly implemented end-to-side anastomotic configurations, with and without proximal outflow. Specifically, sites of significant particle interactions with the vascular surface have been identified by a novel near-wall residence time (NWRT) model for platelets, which includes shear stress-based factors for platelet activation as well as endothelial cell expression of thrombogenic and anti-thrombogenic compounds. Results indicate that the composite NWRT model for platelet-wall interactions effectively captures a reported shift in significant IH formation from the arterial floor of a relatively high-angle (30 deg) graft with no proximal outflow to the graft hood of a low-angle graft (10 deg) with 20% proximal outflow. In contrast, other WSS-based hemodynamic parameters did not identify the observed system-dependent shift in IH formation. However, large variations in WSS-vector magnitude and direction, as encapsulated by the WSS-gradient and WSS-angle-gradient parameters, were consistently observed along the IH-prone suture-line region. Of the multiple hemodynamic factors capable of eliciting a hyperplastic response at the cellular level, results of this study indicate the potential significance of platelet-wall interactions coinciding with regions of low WSS in the development of IH.

Segregation of Flowing Blood: Mathematical Description

“…The results of direct numerical calculations at varied d/a ratio are in agreement with these estimates of I [43]. Their approximation by polynomial in powers of Λ and d/a is used in modern Lagrangian models of single particle motion, such as designed to simulate platelet and monocyte motion in the blood flow for calculating the lateral force acting on them [44][45] ) where inertia of the fluid is negligibly small and rigid particles fail to migrate [1,3,20,26,27,29,47]. The velocity of this migration grows with increasing relative size and deformability of the particle, viscosity of the medium, and shear rate.…”

“…The platelet velocity may be assumed to be equal to the medium velocity (solutions of the Navier-Stokes equations (4.2-4.5)) [78,79] or computed taking account of the forces (2.2) and (2.5) [44][45][46]. The discrete element method (DEM, DPD) mentioned in Section 3.2 provides for an essentially different description of the fluid.…”

Numerical Simulation of Physiological Blood Flow in 2-way Coronary Artery Bypass Grafts

“…Disease formation at the suture-line can be attributed to surgical injury, material mismatch and the abnormal flow patterns around the anastomosis [11][12][13][14][15]. Loth et al suggest that IH is initiated along the suture-line because of mural injury Figure 1.…”

Full-hexahedral structured meshing for image-based computational vascular modeling

“…With the segmentation process the geometry of the vascular segments of interest is extracted from the medical image and usually stored as a set of triangles in STL (stereolithography) format [6]. Owing to the geometrical complexity of the patient-specific domain defined by the STL surface, automatic meshing schemes using tetrahedral elements have been widely preferred for image-based analysis, both in Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) applications, while structured hexahedral meshes have been rarely adopted or limited to simple geometries [7][8][9][10][11].…”