Computational Evaluation of Wall Shear Stress Experienced by Endothelial Tip Cells along Capillary Sprouts

Abstract

Shear stress is commonly implicated as a regulator of angiogenesis. However, critical questions remain unanswered. Do endothelial cells within a capillary sprout lumen experience shear stress? Can tip cells that extend past the sprout lumen experience shear stress? A full understanding of how shear stresses influence endothelial cell phenotype and function during angiogenesis requires the identification of local stress distribution along capillary sprouts. However, the actual shear stress magnitudes experienced by endothelial cells remain unknown. Motivated by the hypothesis that endothelial tip cells can experience physiological shear stress, the objective of this study was to estimate shear stress magnitudes due to local interstitial flow along endothelial tip cells that extend past capillary sprout lumens. A computational fluid dynamics model was used to estimate flows within a blind-ended vessel, transendothelial flow across the vessel wall, and flow within the surrounding perivascular space. The two-dimensional axisymmetric model consisted of four regions: vessel lumen, vessel wall, perivascular space, and interstitium. The vessel wall was assumed to be porous media with 0.3 μm thickness. Blood plasma was represented as an incompressible Newtonian fluid with density and viscosity equal to 1050 kg/m3 and 1.2 cP, respectfully. Shear stresses along the wall of the tip cell extending past the lumen were calculated for varying sprout lengths (50, 200, and 400 μm), perivascular space channel width (1, 4, and 9 μm), and hydraulic conductivities (1.35 and 6.75 x10-10 ms-1 Pa-1). Model parameters and geometric dimensions were selected based on previously reported literature values. Velocity profiles confirmed transmural flow across the vessel wall, nearly parabolic flow within the perivascular space, and velocity gradients along the tip cell. Increasing sprout length, increasing permeability, and decreasing perivascular space increased shear stress values with the perivascular space parameter being the major influencer. Maximum shear stresses along tip cells were consistently higher than the stresses within the sprout lumen. Wall shear stresses within the lumen ranged from 0.02 to 0.52 dyne/cm2 at the sprout entrance and linearly decreased to near zero along the sprout length. Tip cell wall shear stress due to interstitial flow ranged from 0.19 to 4.65 dyne/cm2. The results suggest that wall shear stress values along tip cells can reach physiological relevant values depending on parameter combinations. Our computational estimates motivate new questions related to whether increased shear stresses along tip cells versus luminal cells contribute phenotypic and function signatures of tip cells.