The Influence Of Shear Stress On Restenosis

Wall shear stress (WSS) is the (tangential) drag force acting on the luminal wall, induced by blood flow, normalized to wall area. As WSS is defined as force/area, its dimension equals that of pressure, i.e., N/m2 or Pa. An older, frequently used unit for shear stress, i.e., dyne/cm2 relates to Pa according to 1 Pa = 10 dyne/cm2. WSS on the endothelium (Fig. 1) can be calculated from the local shear rate (s−1) times blood viscosity (μ) (Pa/s). Shear rate is the spatial blood velocity gradient ([m/s]/m). Especially near the vessel wall, generally large velocity gradients between adjacent fluid layers exist and the shear stress is at its highest value. In a simple straight tube the Hagen-Poiseuille formula (WSS = 4μQ/πR3, with μ viscosity, R tube radius and Q flow) can be applied for steady laminar viscous flow. A normal WSS range of 0.68 ± 0.2 Pa was derived from Doppler based velocity measurements in angiographically normal coronary Fig. 1.  Top: flow velocity profile in axial cross-section. Over a very small distance (bottom) velocity increases linearly with distance and wall shear rate (velocity difference/distance) approaches vd/d. arteries of 21 patients (1). Considering the fact that the flow in the investigated branches varied from 6 to 123.2 mL/min, while blood viscosity was assumed constant (3.5 mPa/s), the surprisingly narrow range of shear stress values clearly demonstrates the efficacy of the regulation of coronary lumen size by WSS.