Correction to flow rate--pressure drop relation in coronary angioplasty: steady streaming effect

The changed flow pattern of pulsatile blood flow in a catheterized stenosed artery has been studied through a mathematical model. The study takes into account the effect of the movement of the flexible catheter influenced by the pulsatile nature of the flow. The contribution of the steady streaming effect brings into focus the existence of a non-zero mean pressure drop in addition to the one predicted by the linear theory -- a fact overlooked by the previous authors. Thus our results are intended to provide a correction to the mean pressure drop usually calculated by neglecting the non-linear inertia terms. The calculations based on the geometry and the flow conditions representing a real physiological situation as closely as possible suggest that depending upon the values of k (where k is the ratio of the catheter size to vessel size) ranging from 0.2 to 0.5 mean pressure drop increases for any frequency parameter. In addition, it is found that depending upon the material properties, a thin catheter experiencing small oscillations due to the flow conditions is likely to influence in the same way as a thicker catheter which remains fairly stationary inside the artery. The results are sensitive to the shape of the wall geometry and will be different for different wall geometries even if the cross-sectional area reduction at the peak of stenosis is kept the same. Interesting streamline patterns depict distinct boundary layer characteristics both at the artery wall and catheter wall. Finally, the effect of catheterization and its movement on various physiologically important flow characteristics-mean pressure drop, impedance, wall stress is studied for different range of catheter size and frequency parameter.