Dash R K, Jayaraman G, Mehta K N
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi.
J Biomech. 1999 Jan;32(1):49-61. doi: 10.1016/s0021-9290(98)00142-0.
The fluid mechanics of blood flow in a catheterized curved artery with stenosis is studied through a mathematical analysis. Blood is modelled as an incompressible Newtonian fluid and the flow is assumed to be steady and laminar. An approximate analytic solution to the problem is obtained through a double series perturbation analysis for the case of small curvature and mild stenosis. The effect of catheterization on various physiologically important flow characteristics (i.e. the pressure drop, impedance and the wall shear stress) is studied for different values of the catheter size and Reynolds number of the flow. It is found that all these flow characteristics vary markedly across a stenotic lesion. Also, increase in the catheter size leads to a considerable increase in their magnitudes. These results are used to obtain the estimates of increased pressure drop across an arterial stenosis when a catheter is inserted into it. Our calculations, based on the geometry and flow conditions existing in coronary arteries, suggest that, in the presence of curvature and stenosis, and depending on the value of k (ratio of catheter size to vessel size) ranging from 0.1 to 0.4, the pressure drop increases by a factor ranging from 1.60 to 5.16. But, in the absence of curvature and stenosis, with the same range of catheter size, this increased factor is about 1.74-4.89. These estimates for the increased pressure drop can be used to correct the error involved in the measured pressure gradients using catheters. The combined effects of stenosis and curvature on flow characteristics are also studied in detail. It is found that the effect of stenosis is more dominant than that of the curvature. Due to the combined effect of stenosis, curvature and catheterization, the secondary streamlines are modified in a cross-sectional plane. The insertion of a catheter into the artery leads to the formation of increased number of secondary vortices.
通过数学分析研究了存在狭窄的插入导管的弯曲动脉中血流的流体力学。血液被建模为不可压缩的牛顿流体，并且假定流动是稳定且层流的。对于小曲率和轻度狭窄的情况，通过双重级数摄动分析获得了该问题的近似解析解。针对不同的导管尺寸值和血流雷诺数，研究了导管插入对各种生理上重要的流动特性（即压降、阻抗和壁面剪应力）的影响。发现所有这些流动特性在狭窄病变处有显著变化。此外，导管尺寸的增加会导致其大小显著增加。这些结果用于获得当将导管插入动脉狭窄处时跨狭窄处压降增加的估计值。基于冠状动脉中存在的几何形状和流动条件进行的计算表明，在存在曲率和狭窄的情况下，并且取决于k（导管尺寸与血管尺寸的比值）在0.1至0.4范围内的值，压降增加的倍数在1.60至5.16之间。但是，在不存在曲率和狭窄的情况下，对于相同范围的导管尺寸，这个增加倍数约为1.74 - 4.89。这些跨狭窄处压降增加的估计值可用于校正使用导管测量压力梯度时所涉及的误差。还详细研究了狭窄和曲率对流动特性的综合影响。发现狭窄的影响比曲率的影响更占主导。由于狭窄、曲率和导管插入的综合作用，横截面平面中的二次流线会发生改变。将导管插入动脉会导致形成更多数量的二次涡旋。
