Moore J E, Weydahl E S, Santamarina A
Mechanical Engineering Department, Biomedical Engineering Institute, Florida International University, 10555 West Flagler Street, Miami, FL 33174, USA.
J Biomech Eng. 2001 Apr;123(2):129-33. doi: 10.1115/1.1351806.
The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (delta), normalized change in radius of curvature (epsilon), and a Womersley parameter (alpha). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of epsilon delta alpha > 0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.
通过对冠状动脉弯曲管模型中的血流进行计算研究，以确定随时间变化的曲率对与动脉粥样硬化发展相关的血流模式的重要性。管的入口固定，而曲率半径以1或5Hz的频率随时间呈正弦变化。来自其他研究的血管造影数据表明，曲率半径波形包含高达6Hz的显著频谱成分。总体血流模式与在固定弯曲管中观察到的相似；速度剖面偏向外壁，出现二次流模式等。通过将壁面剪切率幅值与在静态平均曲率半径处计算的剪切率进行归一化，来表示随时间变化的曲率对壁面剪切率变化的影响。结果发现，对于平均曲率比为0.08且曲率半径变化50%的情况，壁面剪切率在曲率中壁处的变化幅度高达平均壁面剪切率的94%。准静态方法不能很好地预测5Hz变形的影响。发现归一化内壁剪切率幅值的最大值与一个无量纲参数成比例关系良好，该参数相当于平均曲率比（δ）、曲率半径归一化变化量（ε）和一个沃默斯利参数（α）的乘积。该参数在预测管内其他位置的幅值时不太成功，因此需要进行更多研究。静态几何形状能很好地预测平均壁面剪切率。这些结果表明，动态曲率在确定经受εδα>0.05变形水平的冠状动脉内壁剪切率方面起着重要作用。准静态方法并不总是能预测这些影响。这些结果为构建更符合实际的冠状动脉血流模型以用于动脉粥样硬化发生研究提供了指导。
