Coronary artery bypass graft (CABG) surgery represents the standard treatment of advanced coronary artery disease (CAD). Since the pioneering work of Favaloro , various grafts and different surgical techniques have been investigated. Regarding anastomoses, two major types exist to connect the graft to the coronary artery, i.e. by using an end-to-side or a side-to-side anastomosis. Although the latter has been reported to provide some advantages over individual grafting with end-to-side anastomosis [2-4], the sequential grafting technique has often been criticized because of differences in the patency rates of the two types of anastomosis [2,5,6]. The long-term clinical outcome after myocardial revascularization is dependent on graft patency. In venous CABG, however, accelerated atherosclerosis has been repetitively reported . During the first year after CABG surgery up to 15% of venous grafts occlude, between 1 and 6 years the graft attrition rate is 1% to 2% per year, and between 6 to 10 years it is 4% per year. By 10 years after surgery only 60% of vein grafts are patent and only 50% of patent vein grafts are free of significant stenosis .
Neointimal hyperplasia, defined as the accumulation of smooth muscle cells and extracellular matrix in the intimal compartment, is the major disease process in venous CABG in the first year after surgery and sets the foundations for later development of graft atheroma . In support of this proposal, the American Heart Association Council on Arteriosclerosis has defined the localized areas of adaptive neointimal hyperplasia as atherosclerosis prone regions . During the first month after CABG surgery vein graft attrition results from thrombotic occlusion , while later on the dominant process is atherosclerotic obstruction occurring on a foundation of neointimal hyperplasia . Although the risk factors predisposing to vein graft atherosclerosis are broadly similar to those recognized for native CAD, the pathogenic effects of these risk factors are amplified by inherent deficiencies of the vein as a conduit when transposed into the coronary arterial circulation .
In attempts to prevent acute and late graft occlusion, much effort has been invested in identifying the etiology of anastomotic neointimal hyperplasia and the plausibility of its prevention. Hypotheses related to this subject include the concept of compliance mismatch between graft and host artery , high frequency flow and wall shear stress (WSS)  as well as abnormal flow dynamics at the distal anastomosis . Sottiurai et al.  have compared in an animal model the development of neointimal hyperplasia in end-to-side versus side-to-side anastomoses. Their study revealed that neointimal hyperplasia was present at the heel, toe, and floor of the end-to-side but not in the side-to-side anastomoses. Since compliance mismatch was not at issue in their model by using autogenous femorofemoral bypass grafts, the geometry of the distal anastomosis was attributed to be the causal factor. The configuration of end-to-side anastomosis is not a common occurrence in the primate cardiovascular system except for a patent "ductus arteriosus Botalli" .
Hemodynamic patterns at distal CABG anastomoses are thought to exhibit flow separation, recirculation and moving stagnation zones. Such flow features correspond typically to low time averaged WSS, long residence times, shear oscillation and increased spatial WSS gradients. These are the main hemodynamic features that have been connected with atherogenesis and intimal hyperplasia [17,18]. In a recent review Kassab and Navia  put forward the homeostasis hypothesis as the underlying mechanism of graft failure. It is postulated that there is a mechanical homeostatic state for each blood vessel. Growth and remodeling takes place to abate perturbations from this state, such as when a vein segment is used in CABG. The remodeling procedure can fail or lead to a non-physiological state when the incurred perturbations are sufficiently large. Hemodynamic flow assessment in coronary arteries and CABGs is commonly performed with intravascular Doppler ultrasound . However, this approach is invasive and the introduction of an ultrasound-catheter leads to flow disturbances thus interfering with the measurements . Lately, phase-contrast magnetic resonance imaging (PC-MRI)  provides a non-invasive means of in-vivo three dimensional instantaneous velocity measurements on selected arterial cross-sections at a sufficient resolution.
An alternative to invasive or non-invasive flow measurements is the simulation of blood flow by using computational fluid dynamics (CFD) and/or ex-vivo experimental flow setups. Numerical studies on physiological coronary flow as well as on CABG flow have been published extensively during the last 15 years. Steinman  presented a transient two dimensional flow simulation within a rigid 45 degree end-to-side anastomosis model. His results indicated elevated instantaneous WSS values at the toe and heel of the graft-host junction as well as along the host artery bed. In 1998 Ethier  simulated three dimensional unsteady flows in a symmetrical 45 degree end-to-side configuration with solid walls. It was shown that the perianastomotic WSS distributions are influenced by a complex interplay between secondary flow effects and the unsteadiness of the graft inflow waveform. An authoritative numerical description of the flow separation patterns of 45 degree junctions was given in  under steady flow conditions for a wide range of inlet Reynolds (Re) numbers, 250 – 1650. This study utilized an adaptive mesh refinement scheme to ensure grid independency.
Research on the hemodynamics of anastomoses has largely focused on determining the influence of the geometric characteristics of end-to-side configurations on WSS distributions. Fei  presented a series of steady flow simulations for a set of anastomosis angles ranging from 20 to 70 degrees. More recently Freshwater  utilized pulsatile flow boundary waveforms typical of a left internal mammary artery graft to the left anterior descending coronary artery scenario. They showed that higher anastomotic angles result in higher WSS magnitude values and flow oscillation around the toe and along the bed of the host branch. In all of the studies referenced so far, the centerlines of the graft and the host vessel lie within the same plane therefore forming planar configurations. Sherwin  investigated the influence of out of plane geometry in stiff end-to-side anastomosis models under steady and Papaharilaou  under transient flow conditions. Such configurations are closer to reality and result in non-symmetric flow fields. In general, the anastomosis bed was affected the most with reduced peak WSS values in comparison to similar planar models, while the mean oscillatory WSS magnitude was also shown to decrease. In most of the aforementioned investigations the native coronary or host vessel was fully occluded. Several researchers have addressed the issue of prograde and/or retrograde flow through the native coronary artery, as in [30,31] under steady flow conditions and in  for pulsatile flow. In order to assess the potential role of activated platelets in the pathogenesis of intimal hyperplasia and/or thrombogenesis, numerical models have tried to quantify shear exposure and near wall residence times [33,34]. Finally, Sankaranarayanan [35,36] presented two studies, in a planar and a non-planar three dimensional CABG model respectively, that included the proximal anastomosis to the aorta.
It is worth noticing that most of the published CFD studies on anastomosis hemodynamics have been evaluated versus equivalent flow experiments by utilizing a variety of flow visualization, velocity and WSS measurement techniques such as in [37-40]. Combined investigations utilizing CFD and PC-MRI on coronary and bypass flows are of particular interest because of the potential of MRI in providing in-vivo velocity measurements as well as anatomical information . The vast majority of the above mentioned investigations focused on the hemodynamics of end-to-side anastomosis configurations. Bonert  examined the hemodynamics of side-to-side CABG anastomosis in solid idealized geometric models. They concluded that the parallel form of side-to-side anastomosis, as opposed to a non-parallel one, is better suited to maintain graft patency. A comparison between side-to-side and end-to-side anastomosis showed increased hemodynamic risk in the former approach due to the presence of larger low WSS areas.
Purpose of the present investigation
Advances in the CFD software and its corresponding hardware along with medical imaging are leading to the generation of increasingly reliable computational models. We can retrace a similar development into the fluid dynamics investigations of physiological coronary flow. Intracoronary flow can now be addressed in anatomically accurate configurations ranging from stiff multi-branched models  to moving and compliant arterial sections . The present study investigated hemodynamic features of CABG anastomoses using patient-specific data. Pulsatile blood flow in venous CABGs was simulated using CFD on solid patient-specific geometric models based on in-vivo CT coronary angiography datasets. We assessed differences in WSS, mass flow, and flow patterns in venous conduits with end-to-side compared to side-to-side anastomosis.