Coronary artery bypass graft (CABG) is a routine surgical treatment for ischemic and infarcted myocardium. A large number of CABG fail postoperatively because of intimal hyperplasia within months or years. The cause of this failure is thought to be partly related to the flow patterns and shear stresses acting on the endothelial cells. An accurate representation of the flow field and associated wall shear stress (WSS) requires a detailed three-dimensional (3D) model of the CABG. The purpose of this study is to present a detailed analysis of blood flow in a 3D aorto/left CABG, bypassing the occluded left anterior descending coronary (LAD) artery. The analysis takes into account the influence of the out-of-plane geometry of the graft. The finite volume technique was employed to model the 3D blood flow pattern to determine the velocity and WSS distributions. This study presents the flow field distributions of the velocity and WSS at four instances of the cardiac cycle, two in systole and two in diastole. Our results reveal that the CABG geometry has a significant effect on the velocity distribution. The axial velocity profiles at different instances of the cardiac cycle exhibit strong skewing; significant secondary flow and vortex structures are seen in the in-plane velocity patterns. The maximum WSS on the bed of the occluded LAD artery opposite to the graft junction is 14 Pa in middiastole, whereas there is a significantly lower and more uniform distribution of WSS on the bed of the anastomosis. The present results indicate that nonplanarity of the blood vessel along with the inflow conditions has a substantial effect on the fluid mechanics of CABG that contribute to the patency of graft.
Idealized geometries of bypass grafts have been constructed to analyze the blood flow in an aorto-coronary bypass graft system. In this paper we discuss the influence of the realistic bypass graft geometry for the in-plane and out-of-plane aorto-left bypass graft models on the wall shear stress distribution. In the in-plane aorto-left coronary bypass graft model we have the centerlines of the aorta, the left coronary vessel and the bypass graft to lie in the same plane (planar geometry) where as in the out-of-plane model the centerlines of the vessels no longer lie in a constant plane (non-planar geometry). Computational fluid dynamic (CFD) studies are carried out using the commercial software FLUENT. It is known that the coronaries are well perfused during the diastole and hence even though simulations are performed at different instances (both the systole and diastole phase) of the cardiac cycle, we have demonstrated the wall shear stress distribution in the distal anastomotic section for both the models at two specific instances of the diastolic phase, namely, early diastole (t=0.45 s) and mid-diastole (t=0.7 s). Our results reveal that in comparison to the in-plane model, the wall shear stress magnitude in the out-of-plane model is greatly reduced at the bed of the anastomosis. Thus a subtle change in the geometry can affect the flow field significantly that may promote graft patency.
It is known that the tremendous internal pressure build-up in the left ventricle (LV) cavity during isovolumic contraction is due to the contraction of the spirally woven myocardial fibers. In this paper, a biomathematical model is developed to investigate the fiber angle using the theory of elasticity. Simultaneously, another simplified model in order to reduce the mathematical complexity was also developed to determine the fiber angle. The results of these two models showed that both the myocardial fiber angles are in same magnitude.
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