Computational model of blood flow in the aorto-coronary bypass graft.

BACKGROUND: Coronary artery bypass grafting surgery is an effective treatment modality for patients with severe coronary artery disease. The conduits used during the surgery include both the arterial and venous conduits. Long- term graft patency rate for the internal mammary arterial graft is superior, but the same is not true for the saphenous vein grafts. At 10 years, more than 50% of the vein grafts would have occluded and many of them are diseased. Why do the saphenous vein grafts fail the test of time? Many causes have been proposed for saphenous graft failure. Some are non-modifiable and the rest are modifiable. Non-modifiable causes include different histological structure of the vein compared to artery, size disparity between coronary artery and saphenous vein. However, researches are more interested in the modifiable causes, such as graft flow dynamics and wall shear stress distribution at the anastomotic sites. Formation of intimal hyperplasia at the anastomotic junction has been implicated as the root cause of long- term graft failure. Many researchers have analyzed the complex flow patterns in the distal sapheno-coronary anastomotic region, using various simulated model in an attempt to explain the site of preferential intimal hyperplasia based on the flow disturbances and differential wall stress distribution. In this paper, the geometrical bypass models (aorto-left coronary bypass graft model and aorto-right coronary bypass graft model) are based on real-life situations. In our models, the dimensions of the aorta, saphenous vein and the coronary artery simulate the actual dimensions at surgery. Both the proximal and distal anastomoses are considered at the same time, and we also take into the consideration the cross-sectional shape change of the venous conduit from circular to elliptical. Contrary to previous works, we have carried out computational fluid dynamics (CFD) study in the entire aorta-graft-perfused artery domain. The results reported here focus on (i) the complex flow patterns both at the proximal and distal anastomotic sites, and (ii) the wall shear stress distribution, which is an important factor that contributes to graft patency. METHODS: The three-dimensional coronary bypass models of the aorto-right coronary bypass and the aorto-left coronary bypass systems are constructed using computational fluid-dynamics software (Fluent 6.0.1). To have a better understanding of the flow dynamics at specific time instants of the cardiac cycle, quasi-steady flow simulations are performed, using a finite-volume approach. The data input to the models are the physiological measurements of flow-rates at (i) the aortic entrance, (ii) the ascending aorta, (iii) the left coronary artery, and (iv) the right coronary artery. RESULTS: The flow field and the wall shear stress are calculated throughout the cycle, but reported in this paper at two different instants of the cardiac cycle, one at the onset of ejection and the other during mid-diastole for both the right and left aorto-coronary bypass graft models. Plots of velocity-vector and the wall shear stress distributions are displayed in the aorto-graft-coronary arterial flow-field domain. We have shown (i) how the blocked coronary artery is being perfused in systole and diastole, (ii) the flow patterns at the two anastomotic junctions, proximal and distal anastomotic sites, and (iii) the shear stress distributions and their associations with arterial disease. CONCLUSION: The computed results have revealed that (i) maximum perfusion of the occluded artery occurs during mid-diastole, and (ii) the maximum wall shear-stress variation is observed around the distal anastomotic region. These results can enable the clinicians to have a better understanding of vein graft disease, and hopefully we can offer a solution to alleviate or delay the occurrence of vein graft disease.

A novel coronary artery bypass graft design of sequential anastomoses.

In this paper, the hemodynamics in a three-dimensional out-of-plane sequential bypass graft model is first investigated. Based on the advantageous flow characteristics observed within the side-to-side (STS) anastomosis in the sequential bypass graft simulation, a new CABG coupled-sequential anastomosis configuration is designed, entailing coupled STS and end-to-side (ETS) anastomotic components. In this new CABG design, the flow fields and distributions of various wall shear stress parameters within the STS and ETS anastomotic regions are studied, and compared to those of the conventional distal anastomosis, by means of computational fluid dynamics simulation of pulsatile Newtonian blood flow. Simulation results demonstrate that the new sequential anastomoses model provides: (i) a more uniform and smooth flow at the ETS anastomosis, without any stagnation point on the artery bed and vortex formation in the heel region of the ETS anastomosis within the coronary artery; (ii) a spare route for the blood flow to the coronary artery, to avoid re-operation in case of re-stenosis in either of the anastomoses; and (iii) improved distribution of hemodynamic parameters at the coronary artery bed and in the heel region of the ETS anastomosis, with more moderate shear stress indices. These advantages of the new design over the conventional ETS anastomosis are influenced by the occlusion ratio of the native coronary artery, and are most prominent when the proximal segment of the coronary artery is fully occluded. By varying the design parameters of the anastomotic angle and distance between the two anastomoses, the superior coupled STS-ETS anastomoses design is found to have the anastomotic angle of 30° and 30 mm distance between the two (STS and ETS) components.

Analysis of blood flow in an out-of-plane CABG model.

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.

Role of sphingosine kinase in the expression of adhesion molecules on monocytes induced by tumor necrosis factor-alpha (relevant to atherosclerosis).

TNFα stimulates SPHK in the monocyte, which leads to the expression of adhesion molecules on the cell surface. The adhesion of leukocytes to the endothelium is one of the early stages of the onset of atherosclerosis. In this paper, we have delineated the TNFα-induced and SPHK-dependent signaling pathway. In addition, we have developed a biomathematical model to qualify the SPHK time-dependent activity at a specific site in the cell upon TNFα stimulation. Thus, this study provides a biochemical and mechanistic approaches to the understanding of leukocyte-endothelial attachment, so that measures could be designed to minimize the onset of atherosclerosis.

Influence of aorto-left coronary bypass graft geometry on wall shear stress distribution.

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.

Determination of the left ventricular myofiber angle analytically and its significance.

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.