Unsteady simulation of distal blood flow in an end-to-side anastomosed coronary bypass graft with stenosis

In this paper, we report on the unsteady state modeling of blood flow in an end-to-side anastomosed bypass graft, which has a stenosis upstream from the junction. In coronary artery bypass grafting/surgery (CABG), new arteries are created in order to provide blood to the heart using other blood vessels as conduits to bypass the blocked section in the patient's coronary arteries. The failure of coronary artery bypass procedures has been attributed to both intimal hyperplasia (IH) and atherosclerosis. It is believed that these two phenomena are, in turn, related to the local hemodynamic factors. In this work, a three-dimensional computational fluid dynamics analysis is used to simulate the physiological blood flow through a model of a stenosed coronary bypass graft with the realistic assumption of non-Newtonian flow for human blood. For different flow repartitions and at different times of the cycle, both the recirculating areas and wall shear stress (WSS) are studied. Based on the different distribution of flow rates in the bypass graft and the host artery, the flow features are investigated and the influence of non-Newtonian behavior is discussed in terms of separation points, reattachment points, and the wall shear stresses. Various differences are observed based on the assumption of non-Newtonian behavior of blood, which have not been reported before when a simplified Newtonian approach is utilized.     

Hemodynamic effects of the geometric dimensions of graft vessels in coronary artery bypass graft models.

The objectives of this investigation are to evaluate the rheologic properties in atherosclerotic disease treated with the various coronary artery bypass graft (CABG) models by numerical analysis, we used four different CABG models for the assessment of spatial fluctuation in wall shear stress, pressure variation and mass flow rate with Carreau model and Navier-Stokes equation. Wall shear stress was higher in a naturally tapered model (model 1) and a constant (non-tapered) diameter of the graft vessel the same as the distal LAD (model 4) than in others. Pressure variation along the native coronary artery and graft vessels was higher in a model 4, model 1 than in a reverse tapering model (model 2) and a constant diameter of the graft vessel the same as the proximal LAD (model 3). The mass flow rate of the distal part (kg/sec,.m(o)) was the highest in model 3. This study suggests that in vitro spatial simulation following CABG revealed that small caliber or tapered graft vessels have adverse hemodynamic effects on the native and graft vessels. By this technique it is possible to simulate the optimal distribution of local hemodynamic variables in patients treated with CABG, also to minimize the degeneration of graft vessel.     

Influence of graft-host diameter ratio on the hemodynamics of CABG

The graft-host diameter ratios have impacts on the flow patterns of bypass graft. In order to clarify the influence of graft-host diameter ratios on the flow patterns and the wall shear stress in coronary artery bypass graft (CABG), the pulsatile blood flows in three CABG models, with the graft diameter larger than, equal to and smaller than that of the coronary artery, were simulated with finite element method. The temporal-spatial distributions of flow patterns, wall shear stresses (WSS), wall shear stress gradients (WSSG), oscillating shear index and shear stress ratio were depicted and compared. Of the three models evaluated, large model can bring about better hemodynamics to some extent with relatively large positive longitudinal velocity, uniform and large WSS, and small WSSG. The results suggest that larger or isodiametric graft is favorable. However, no distinct difference of WSS based temporal parameters was found between all the three models. Alternative anastomotic designs are necessary for the improvement of CABG patency rates.     

Estimation of wall shear stress in bypass grafts with computational fluid dynamics method

Coronary artery bypass graft (CABG) operation for coronary artery disease with different types of grafts has a large clinical application world wide. Immediately after this operation patients are usually relieved of their chest pain and have improved cardiac function. However, after a while, these bypass grafts may fail due to for example, neointimal hyperplasia or thrombosis. One of the causes for this bypass graft failure is assumed to be the blood flow with low wall shear stress. The aim of this research is to estimate the wall shear stress in a graft and thus to locate areas were wall shear stress is low. This was done with the help of a blood flow computer model. Post-operative biplane angiograms of the graft were recorded, and from these the three-dimensional geometry of the graft was reconstructed and imported into the computational fluid dynamics (CFD) program FLUENT. The stationary diastolic flow through the grafts was calculated, and the wall shear stress distribution was estimated. This procedure was carried out for one native vessel and two different types of bypass grafts. One bypass graft was a saphenous vein and the other one was a varicose saphenous vein encased in a fine, flexible metal mesh. The mesh was attached to give the graft a defined diameter. The computational results show that each graft has distinct areas of low wall shear stress. The graft with the metal mesh has an area of low wall shear stress (< 1 Pa, stationary flow), which is four times smaller than the respective areas in the other graft and in the native vessel. This is thought to be caused by the smaller and more uniform diameter of the metal mesh-reinforced graft.     

具有不同移植管-宿主动脉直径比的冠状动脉搭桥术的血流动力学仿真比较

为了说明移植管-宿主动脉直径比对冠状动脉搭桥术的流场及壁面切应力的影响，构造了三个具有不同移植管-宿主动脉直径比的冠状动脉搭桥术模型，三个模型的移植管直径分别小于、等于和大于宿主动脉的直径；利用有限单元数值模拟方法对三个模型中的生理性脉动血流进行了仿真分析；对流场、壁面切应力及其相关系数的时空分布进行了显示和比较。结果表明，大直径比的模型具有相对较大的纵向速度、大而均匀的壁面切应力以及小的壁面切应力梯度，从而在一定程度上改善了血流动力学；在搭桥术应用中采用大于或等于1的直径比是可取的。然而，在三个模型中，与壁面切应力相关的时间参数并没有显著差别。为了提高冠状动脉搭桥术的畅通率，设计新的缝合结构是很有必要的。     

Computational Investigation of Hemodynamics in Fully Stenosed CABG

Coronary Artery Bypass Graft (CABG) is an important surgical treatment for critically stenosed arteries. Unfortunately restenosis always occurs after CABG surgery, which bring about surgery failure, lntimal thickening in the CABG distal anastomosis has been implicated as the major cause of restenosis and long-term graft failure. The nonuniform hemodynamics including disturbed flows, recirculation zones, oscillating wall shear stress, and long particle residence time were thought to be the possible etiologies. Numerical simulation was proved to be of great help and guidance meaning for the biofluid mechanics research and the CABG surgical plan. The present study was based on the hypothesis that the geometry configuration of CABG could greatly influence the hemodynamics in the vicinity of anastomosis. The hemodynamic features of two geometry models of end-to-side CABG were studied and compared. One simulated a conventional CABG with 1-way bypass graft, and the other simulated a modified CABG with symmetric 2-way bypass graft. The numerical investigations of hemodynamics in these two models with fully stenosed coronary arteries were accomplished using finite element method. The temporal and spatial distributions of hemodynamics were analyzed and compared. Results showed that the presence of symmetric 2-way bypass graft was of reasonable and favorable hemodynamics than 1-way bypass graft. The modified CABG model created a more hemodynamically efficient streamlined environment with higher mean and maximum axial velocities and lower radial velocities than the conventional 1-way model. Meanwhile, the symmetric 2-way bypass graft was featured with low pressure near the wall, high and uniform WSS in the host artery. All of these were favorable for inhibiting the development of intimal thickening, restenosis, and ultimate failure of the CABG, and it could considerably improve the flow conditions and decrease the probability of intimal hyperplasia and restenosis of CABG.     

单路和双路CABG中血流动力学的比较

为了改善冠状动脉搭桥术后的血流动力学，提出了对称双路搭桥的改进措施。利用有限元分析方法，对冠状动脉搭桥术中单路移植管和对称双路移植管内的生理流动进行了数值模拟，并对两种情况下的血流动力学计算结果进行了比较。计算结果分析了缝合区附近的流场、壁面剪应力等血流动力学因素在心动周期内的时空分布情况。研究结果表明，对称双路搭桥比单路搭桥具有更合理的血流动力学，可以避免动脉粥样硬化的危险性血流动力学因素，从而减少手术再狭窄的发生。     

Influence of Junction Angle Changed Models on Hemodynamic of Coronary Artery Bypass Graft

The restenosis after coronary artery bypass graft(CABG) is attributed to the formation of intimal hyperplasia(IH) at the anastomosis,which is closely related to hemodynamic depend on the geometric model. In order to give a reasonable assessment of the surgery effect and judge the long-term patency rate,the hemodynamic of CABG surgery program is compared with that of surgery design of the junction angle changed.Based on in-vivo CT coronary angiography datasets,the individual geometric model of CABG reconstructed instead of idealized geometric models are applied to simulate the real physiological blood flow utilizing pulsatile flow boundary waveforms in the present study. The simulation results show that the maximum wall shear rate(WSS) value is at the bottom of anastomosis. Moreover,the stagnation zone growing gradually with the greater angle downstream the anastomosis is prone to form the IH,which is consistent with clinical observation. It is proved that the surgery being better suited to maintain graft patency is successful.     

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.     

Compliant model of a coupled sequential coronary arterial bypass graft: effects of vessel wall elasticity and non-Newtonian rheology on blood flow regime and hemodynamic parameters distribution

We have recently developed a novel design for coronary arterial bypass surgical grafting, consisting of coupled sequential side-to-side and end-to-side anastomoses. This design has been shown to have beneficial blood flow patterns and wall shear stress distributions which may improve the patency of the CABG, as compared to the conventional end-to-side anastomosis. In our preliminary computational simulation of blood flow of this coupled sequential anastomoses design, the graft and the artery were adopted to be rigid vessels and the blood was assumed to be a Newtonian fluid. Therefore, the present study has been carried out in order to (i) investigate the effects of wall compliance and non-Newtonian rheology on the local flow field and hemodynamic parameters distribution, and (ii) verify the advantages of the CABG coupled sequential anastomoses design over the conventional end-to-side configuration in a more realistic bio-mechanical condition. For this purpose, a two-way fluid-structure interaction analysis has been carried out. A finite volume method is applied to solve the three-dimensional, time-dependent, laminar flow of the incompressible, non-Newtonian fluid; the vessel wall is modeled as a linearly elastic, geometrically non-linear shell structure. In an iteratively coupled approach the transient shell equations and the governing fluid equations are solved numerically. The simulation results indicate a diameter variation ratio of up to 4% and 5% in the graft and the coronary artery, respectively. The velocity patterns and qualitative distribution of wall shear stress parameters in the distensible model do not change significantly compared to the rigid-wall model, despite quite large side-wall deformations in the anastomotic regions. However, less flow separation and reversed flow is observed in the distensible models. The wall compliance reduces the time-averaged wall shear stress up to 32% (on the heel of the conventional end-to-side model) and somewhat increases the oscillatory nature of the flow. It is found that the effects of wall compliance and non-Newtonian rheology are not independent, and they interact with each other. In spite of the modest influence of wall compliance and non-Newtonian rheology on the hemodynamic parameters distribution, the inclusion of these properties has unveiled further advantages of the coupled sequential anastomoses model over the conventional end-to-side anastomosis which had not been revealed in the previous study with the rigid-wall and Newtonian fluid models. Hence, the inclusion of wall compliance and non-Newtonian rheology in flow simulation of blood vessels can be essential in quantitative and comparative investigations.     

Atrial fibrillation as a contributing factor in the diagnostic algorithm for coronary subclavian steal syndrome and cardiac tamponade following coronary artery bypass graft surgery: a case study

Coronary subclavian steal syndrome (CSSS) is a complication of coronary artery bypass graft (CABG) surgery in patients with coexistent significant subclavian artery stenosis (SAS). It is characterized by a retrograde blood flow through the left internal mammary artery graft from the coronary to subclavian circulation, leading to myocardial ischemia. Current screening for CSSS includes bilateral blood pressure measurement for the detection of a significant inter-arm blood pressure difference. However, the commonly used automated sphygmomanometers have limited accuracy in patients with atrial fibrillation. Consequently, these patients are often underdiagnosed. We present a case of a 73-year-old man with a medical history of atrial fibrillation, peripheral artery disease, and CABG surgery four months before the current event, who came to the emergency department due to progressive dyspnea. The initial diagnostic management showed a large circulatory pericardial effusion, so the patient was admitted to the coronary care unit and underwent pericardial drainage. In the following days, due to a sudden high increase in cardiac troponin, the patient underwent an urgent coronary angiography, which revealed severe left SAS with functional CABG, indicating the occurrence of CSSS. Percutaneous transluminal angioplasty was then performed with an optimal angiographic result. The patient was discharged in good condition with adequate medicament therapy and instructions. This case report highlights atrial fibrillation as a contributing factor for the diagnosis of CSSS and pericardial tamponade after CABG surgery. Furthermore, we suggest a diagnostic approach that can reduce the incidence of both these severe complications.

Coronary subclavian steal syndrome (CSSS) occurs in the presence of subclavian artery stenosis (SAS) or occlusion and represents a reversal of blood flow in the left internal mammary artery (LIMA) bypass graft, which leads to coronary ischemia. It presents as a complication in 2.5–4.5% of patients undergoing coronary artery bypass graft (CABG) surgery. The prevalence is even higher in patients with peripheral artery disease (PAD), who have a 5-fold increased risk of SAS (1,2). It commonly presents as stable angina triggered by left upper extremity activity, but can also manifest as an acute coronary syndrome, acute heart failure, ventricular arrhythmia, or even sudden cardiac death (3). Digital subtraction angiography, the current gold standard in the imaging of CSSS, has lately been increasingly replaced by other diagnostic tools, such as duplex ultrasound (DUS), computed tomography angiography (CTA), and magnetic resonance angiography. The current guidelines recommend the endovascular approach as the first-line treatment of CSSS and vascular surgery as the second option (4).     

Flow studies in three-dimensional aorto-right coronary bypass graft system

This paper presents the fluid dynamics of blood flow in a coronary bypass model of the aorto-right coronary bypass system. Three-dimensional computational fluid dynamic simulations are developed of the blood flow in coronary artery-bypass systems, using the computational fluid dynamics software (FLUENT 6.0.1). These blood flow simulations are performed within small intervals of the cardiac cycle, using input data consisting of physiological measurements of flow rates in the aorta, obtained from earlier studies. We have calculated the flow-field distributions of the velocity and the wall shear stress at four typical instants of the cardiac cycle, two during systole and two during the diastole phase. Plots of velocity vector and the wall shear stress are displayed in the aorto-graft-coronary arterial flow-field domain, providing an insight into the link between fluid dynamics and arterial diseases. The prime regions of disturbed flow patterns are at the entrance into the graft from the aorta and at the exit from the graft into the right coronary artery. Our objective is to obtain an understanding of how the coronary artery is perfused by the graft, and thereby into the factors affecting graft patency.     

Flow studies in three-dimensional aorto-right coronary bypass graft system

This paper presents the fluid dynamics of blood flow in a coronary bypass model of the aorto-right coronary bypass system. Three-dimensional computational fluid dynamic simulations are developed of the blood flow in coronary artery-bypass systems, using the computational fluid dynamics software (FLUENT 6.0.1). These blood flow simulations are performed within small intervals of the cardiac cycle, using input data consisting of physiological measurements of flow rates in the aorta, obtained from earlier studies. We have calculated the flow-field distributions of the velocity and the wall shear stress at four typical instants of the cardiac cycle, two during systole and two during the diastole phase. Plots of velocity vector and the wall shear stress are displayed in the aorto-graft-coronary arterial flow-field domain, providing an insight into the link between fluid dynamics and arterial diseases. The prime regions of disturbed flow patterns are at the entrance into the graft from the aorta and at the exit from the graft into the right coronary artery. Our objective is to obtain an understanding of how the coronary artery is perfused by the graft, and thereby into the factors affecting graft patency.     

In vitro measurements of velocity and wall shear stress in a novel sequential anastomotic graft design model under pulsatile flow conditions

This study documents the superior hemodynamics of a novel coupled sequential anastomoses (SQA) graft design in comparison with the routine conventional end-to-side (ETS) anastomoses in coronary artery bypass grafts (CABG). The flow fields inside three polydimethylsiloxane (PDMS) models of coronary artery bypass grafts, including the coupled SQA graft design, a conventional ETS anastomosis, and a parallel side-to-side (STS) anastomosis, are investigated under pulsatile flow conditions using particle image velocimetry (PIV). The velocity field and distributions of wall shear stress (WSS) in the models are studied and compared with each other. The measurement results and WSS distributions, computed from the near wall velocity gradients reveal that the novel coupled SQA design provides: (i) a uniform and smooth flow at its 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) more favorable WSS distribution; and (iii) 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. This in vitro investigation complements the previous computational studies of blood flow in this coupled SQA design, and is another necessary step taken toward the clinical application of this novel design. At this point and prior to the clinical adoption of this novel design, in vivo animal trials are warranted, in order to investigate the biological effects and overall performance of this anastomotic configuration in vivo.     

Native Coronary Artery and Grafted Artery Spasm Just after Coronary Artery Bypass Grafting: A Case Report

Native coronary artery spasm after coronary artery bypass grafting (CABG) is scarce. It frequently causes disastrous circulatory collapse. We report a 72-yr-old male, who experienced native coronary artery spasm and grafted artery spasm following CABG, which was successfully treated with coronary angiography and intracoronary injection of nitroglycerine.     

Hybrid small-caliber vascular prosthesis for coronary artery bypass grafting: a preliminary study of plasmin-treated fibrin-coated vascular prosthesis

The potential use of plasmin-treated fibrin-coated vascular prosthesis (PF-V) for coronary artery bypass grafting (CABG) in animal models was investigated. PF-V grafts, 3 mm in internal diameter, were studied on 5 sheep in off-pump CABG model and on 18 rabbits in abdominal aortic bypass grafting (AABG) model. Patency, blood flow, angiography, Indium-111 platelet scintigraphy, and histology of the graft were evaluated. In the sheep CABG model, the PF-V grafts were patent for a range of 12 to 22 days without postoperative antiplatelet therapy. Graft flows ranged 58 to 90 ml/min until the day before graft occlusion by thrombus. In rabbit AABG model, the fibrin coating of the PF-V grafts was completely absorbed and replaced with neofibrin net between 7 and 14 days after implantation. Platelet depositions on the graft between 7 and 14 days after implantation were significantly higher than those at other periods (p < 0.05). The small-caliber PF-V graft in sheep CABG model had a good blood flow with high antithrombogenicity in acute phase, but occluded over 2 to 3 weeks without antiplatelet agents after implantation. The current problem of the PF-V graft was a thrombus formation at the time of the degradation of fibrin coating. Further improvements are needed.     

自体腹膜管道替代血管在冠状动脉搭桥手术中的实验应用

目的 采用实验犬的腹膜片制作腹膜管道替代冠状动脉搭桥手术中的传统移植血管,希望为冠状动脉搭桥提供一种理想的血管替代物.方法 随机选用杂种成年犬10头,雌雄不限,麻醉后气管插管行机控呼吸.所有犬经旁正中切口达腹直肌鞘后层取腹膜片,制成腹膜管道在非体外循环下行主动脉与右冠状动脉主干搭桥.采用电磁血流量计测量搭桥前后腹膜管道的血流通畅度.术毕记录实验犬的早期存活比例,饲养至实验结束处死动物,光镜下观察HE染色腹膜管道的病理变化.结果 实验犬的早期死亡比例为10%(1/10),腹膜管道的血流通畅,冠状动脉搭桥手术前后实验犬右冠状动脉的血流量分别为(126±13)、(117±14)ml/min,差异无统计学意义(P>0.05).腹膜管道的组织学形态改变良好,光镜下,未见腹膜管道瘤样扩张,无明显纤维疤痕形成,腹膜管道弹力纤维结构完好,无断裂,腹膜管道与血管吻合口附近有血管内皮细胞衍生.结论 在非体外循环下采用腹膜管道替代传统的移植血管行冠状动脉搭桥创伤小,实验犬存活比例高,冠状动脉血供效果令人满意,有希望成为理想的血管移植替代物.     

Human Saphenous Vein Coronary Artery Bypass Graft Morphology,Geometry and Hemodynamics

Coronary artery bypass graft (CABG) failure has been linked to graft hemodynamics, in particular wall shear stress. This study characterizes the morphology, geometry and wall shear stress patterns in human CABGs. The intimal thickness (IT) in 49 human saphenous vein CABGs was measured by digital light microscopy. The geometry of six saphenous vein CABGs was replicated by post-mortem infusion of Batsons #17 anatomical corrosion casting compound. Graft hemodynamics were evaluated in two flow models, fabricated from the casts, under steady (Re = 110) and pulsatile flow (Re = 110, = 2) conditions. Saphenous vein CABGs in situ for more than 2 months had, on average, the greatest IT on the hood and suture sites of the distal anastomosis. Floor thickening was highly variable and significantly less than IT at the hood, suture site and graft body. All casts showed an indentation along the floor and 5/6 casts displayed a sharp local curvature on the hood. In both flow models, a large increase in wall shear rate occurred on the hood, just proximal to the toe. The local geometry of the hood created this large spatial gradient in wall shear stress which is a likely factor in hood intimal hyperplasia.     

Investigation of hemodynamics during cardiopulmonary bypass: A multiscale multiphysics fluid–structure-interaction study

Neurological complications often occur during cardiopulmonary bypass (CPB). Hypoperfusion of brain tissue due to diminished cerebral autoregulation (CA) and thromboembolism from atherosclerotic plaque reduce the cerebral oxygen supply and increase the risk of perioperative stroke. To improve the outcome of cardiac surgeries, patient-specific computational fluid dynamic (CFD) models can be used to investigate the blood flow during CPB.In this study, we establish a computational model of CPB which includes cerebral autoregulation and movement of aortic walls on the basis of in vivo measurements. First, the Baroreflex mechanism, which plays a leading role in CA, is represented with a 0-D control circuit and coupled to the 3-D domain with differential equations as boundary conditions. Additionally a two-way coupled fluid–structure interaction (FSI) model with CA is set up. The wall shear stress (WSS) distribution is computed for the whole FSI domain and a comparison to rigid wall CFD is made. Constant flow and pulsatile flow CPB is considered.Rigid wall CFD delivers higher wall shear stress values than FSI simulations, especially during pulsatile perfusion. The flow rates through the supraaortic vessels are almost not affected, if considered as percentages of total cannula output. The developed multiphysic multiscale framework allows deeper insights into the underlying mechanisms during CPB on a patient-specific basis.     

Numerical analysis of blood flow distribution in 4- and 3-branch vascular grafts

Trifurcated arch grafts (3-branch grafts) are now being used to repair the thoracic aorta in addition to conventional arch grafts (4-branch grafts). The anatomical shape of the 3-branch graft is different from the original vessel, so it is necessary for clinical application to evaluate blood flow distribution in the graft to assess whether there is adequate blood flow to the target organs. To achieve this, we developed a computational fluid dynamics (CFD) method to evaluate blood flow distribution in the grafts. Aortic blood flow was measured by phase-contrast magnetic resonance imaging (PC-MRI), and flow distribution into the branched vessels was obtained. The MRI image was used to create a patient-specific image model that represents the geometry of the aortic arch. The CFD analysis method was employed to determine a boundary condition of the blood flow analysis in the aorta using a patient-specific image model. We also created simplified models of 4-branch and 3-branch grafts and used our CFD analysis method to compare blood flow distribution among simplified models. It was found that blood flow distribution in the descending aorta was 71.3 % for the 4-branch graft and 67.7 % for the 3-branch graft, indicating that a sum of branching flow in the 3-branch graft was almost the same as the one in the 4-branch graft. Therefore, there is no major concern about implanting a new 3-branch graft. Our CFD analysis method may be applied to estimate blood flow distribution of a newly developed vascular graft prior to its clinical use and provide useful information for safe use of the graft.