Perktold K, Rappitsch G
Institute of Mathematics, Technical University Graz, Austria.
J Biomech. 1995 Jul;28(7):845-56. doi: 10.1016/0021-9290(95)95273-8.
To investigate the effect of the distensible artery wall on the local flow field and to determine the mechanical stresses in the artery wall, a numerical model for the blood flow in the human carotid artery bifurcation has been developed. The wall displacement and stress analysis use geometrically non-linear shell theory where incrementally linearly elastic wall behavior is assumed. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier-Stokes equations for non-Newtonian inelastic fluids. In an iteratively coupled approach the equations of the fluid motion and the transient shell equations are numerically solved using the finite element method. The study shows the occurring characteristics in carotid artery bifurcation flow, such as strongly skewed axial velocity in the carotid sinus with high velocity gradients at the internal divider wall and with flow separation at the outer common-internal carotid wall and at the bifurcation side wall. Flow separation results in locally low oscillating wall shear stress. Further strong secondary motion in the sinus is found. The comparison of the results for a rigid and a distensible wall model demonstrates quantitative influence of the vessel wall motion. With respect to the quantities of main interest, it can be seen, that flow separation and recirculation slightly decrease in the sinus and somewhat increase in the bifurcation side region, and the wall shear stress magnitude decreases by 25% in the distensible model. The global structure of the flow and stress patterns remains unchanged. The deformation analysis shows that the tangential displacements are generally lower by one order of magnitude than the normal directed displacements. The maximum deformation is about 16% of the vessel radius and occurs at the side wall region of the intersection of the two branches. The analysis of the maximum principal stresses at the inner vessel surface shows a complicated stress field with locally high gradients and indicates a stress concentration factor of 6.3 in the apex region.
为了研究可扩张动脉壁对局部流场的影响并确定动脉壁中的机械应力，已建立了人体颈动脉分叉处血流的数值模型。壁位移和应力分析采用几何非线性壳理论，假定壁的行为为增量线性弹性。流动分析应用了非牛顿非弹性流体的与时间相关的三维不可压缩纳维-斯托克斯方程。在迭代耦合方法中，使用有限元法对流体运动方程和瞬态壳方程进行数值求解。研究显示了颈动脉分叉处血流中出现的特征，如颈动脉窦内轴向速度强烈倾斜，在内部分隔壁处具有高速度梯度，在外颈总动脉-颈内动脉壁以及分叉侧壁处出现流动分离。流动分离导致局部低振荡壁面剪应力。还发现窦内有进一步强烈的二次流动。刚性壁模型和可扩张壁模型结果的比较表明了血管壁运动的定量影响。就主要关注的量而言，可以看出，流动分离和再循环在窦内略有减少而在分叉侧区域略有增加，并且在可扩张模型中壁面剪应力大小降低了25%。流动和应力模式的整体结构保持不变。变形分析表明，切向位移通常比法向位移低一个数量级。最大变形约为血管半径的16%，发生在两个分支相交处的侧壁区域。血管内表面最大主应力的分析显示了一个具有局部高梯度的复杂应力场，并表明在顶点区域应力集中系数为6.3。
