Flow in a catheterized curved artery with stenosis

The fluid mechanics of blood how in a catheterized curved artery with steno sis is studied through a mathematical analysis. Blood is modelled as an inc ompressible Newtonian fluid and the flow is assumed to be steady and lamina r. An approximate analytic solution to the problem is obtained through a do uble series perturbation analysis for the case of small curvature and mild stenosis. The effect of catheterization on various physiologically importan t flow characteristics (i.e. the pressure drop, impedance and the wall shea r 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 m arkedly 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 geomet ry 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 cu rvature 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 gradient s using catheters. The combined effects of stenosis and curvature on flow c haracteristics are also studied in detail. It is found that the effect of s tenosis is more dominant than that of the curvature. Due to the combined ef fect of stenosis, curvature and catheterization, the secondary streamlines are modified in a cross-sectional plane. The insertion of a catheter into t he artery leads to the formation of increased number of secondary vortices. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.