A nonlinear method to determine the wall shear stress in the straight artery in vivo

With the aid of Ling and Atabek's ``local flow''assumption for the nonlinear convective acceleration terms of theNavier-Stokes equation governing the pulsatile blood flow in large arteries,a nonlinear method to determine the wall shear stress in straight arterieswas proposed by use of the measured blood viscosity, center-line velocity,blood pressure and arterial radius. Comparing with the results from thelinear method proposed by Liu Zhaorong et al., where the wall shear stresswas calculated using the measured blood viscosity, center-line velocity andaverage arterial radius, the results from the nonlinear method demonstratedthat, no obvious difference exists between the pressure gradients, thevelocity profiles, and the wall shear stresses calculated from the twodifferent methods when the wall motion (\d R/R = 2.4\%) is small, however,an obvious difference occurs when the wall motion is large (\d R/R=12\%).It was concluded that the linear method has high accuracy when the wallmotion is small but the nonlinear effects on the wall shear stress must betaken into consideration when the wall motion becomes large. Because theinputs such as the blood viscosity, the center-line velocity, the bloodpressure and the arterial radius could be measured by use of non-invasiveand/or micro-invasive methods, the nonlinear method provided the methodologybase for the in vivo and/or ex-vivo study of the relationshipbetween the wall shear stress and arterial remodeling.