The influence of out-of-plane geometry on the flow within a distal end-to-side anastomosis

Multi-Objective Optimisation of a Novel Bypass Graft with a Spiral Ridge

The low long-term patency of bypass grafts is a major concern for cardiovascular treatments. Unfavourable haemodynamic conditions in the proximity of distal anastomosis are closely related to thrombus creation and lumen lesions. Modern graft designs address this unfavourable haemodynamic environment with the introduction of a helical component in the flow field, either by means of out-of-plane helicity graft geometry or a spiral ridge. While the latter has been found to lack in performance when compared to the out-of-plane helicity designs, recent findings support the idea that the existing spiral ridge grafts can be further improved in performance through optimising relevant design parameters. In the current study, robust multi-objective optimisation techniques are implemented, covering a wide range of possible designs coupled with proven and well validated computational fluid dynamics (CFD) algorithms. It is shown that the final set of suggested design parameters could significantly improve haemodynamic performance and therefore could be used to enhance the design of spiral ridge bypass grafts.

On the importance of spiral-flow inflow boundary conditions when using idealized artery geometries in the analysis of liver radioembolization: A parametric study

In the last decades, the numerical studies on hemodynamics have become a valuable explorative scientific tool. The very first studies were done over idealized geometries, but as numerical methods and the power of computers have become more affordable, the studies tend to be patient specific. We apply the study to the numerical analysis of tumor-targeting during liver radioembolization (RE). RE is a treatment for liver cancer, and is performed by injecting radiolabeled microspheres via a catheter placed in the hepatic artery. The objective of the procedure is to maximize the release of radiolabeled microspheres into the tumor and avoid a healthy tissue damage. Idealized virtual arteries can serve as a generalist approach that permits to separately analyze the effect of a variable in the microsphere distribution with respect to others. However, it is important to use proper physiological boundary conditions (BCs). It is not obvious, the need to account for the effect of tortuosity when using an idealized virtual artery. We study the use of idealized geometry of a hepatic artery as a valid research tool, exploring the importance of using realistic spiral-flow inflow BC. By using a literature-based cancer scenario, we vary two parameters to analyze the microsphere distribution through the outlets of the geometry. The parameters varied are the type of microspheres injected and the microsphere injection velocity. The results with realistic inlet velocity profile showed that the particle distribution in the liver segments is not affected by the analyzed injection velocity values neither by the particle density. NOVELTY STATEMENT: In this article, we assessed the use of idealized geometries as a valid research tool and applied the use of an idealized geometry to the case of an idealized hepatic artery to study the particle-hemodynamics during radioembolization (RE). We studied three different inflow boundary conditions (BCs) to assess the usefulness of the geometry, two types of particle injection velocities and two types of commercially available microspheres for RE treatment. In recent years, the advent in computational resources allowed for more detailed patient-specific geometry generation and discretization and hemodynamics simulations. However, general studies based on idealized geometries can be performed in order to provide medical doctors with some basic and general guidelines when using a given catheter for a given cancer scenario. Moreover, using an idealized geometry can be a reasonable approach which allows us to isolate a given parameter and control other parameters, so that parameters can be independently assessed. Even though an idealized geometry does not match any patient's geometry, the use of an idealized geometry can be valid when drawing general conclusions that may be useful in patient-specific cases. However, we believe that even if an idealized hepatic artery geometry is used for the study, it is necessary to account for the upstream and downstream tortuosity of vessels through the BCs. In this work, we highlighted the need of modeling the tortuosity of upstream and downstream vasculatures through the BCs.

Computed tomography-based hemodynamic index for aortic dissection

OBJECTIVE

In this study we aimed to propose a new computed tomography-based hemodynamic indicator to quantify the functional significance of aortic dissection and predict post intervention luminal remodeling.

METHODS

Computational hemodynamics and 3D structural analyses were conducted in 51 patients with type B aortic dissection, at initial presentation and at approximately 1 month, 3 months, and 1 year post intervention. A functional index was proposed on the basis of luminal pressure difference. Statistical relationships between the proposed indicator and longitudinal luminal development were analyzed.

RESULTS

The computed luminal pressure difference (true lumen pressure minus false lumen pressure) varied overall from positive to negative along the aorta. The first balance position at which the pressure difference equals 0 was proposed as the functional indicator. A more distally located first balance position indicated better functional status. Implantation of stent graft distally shifted this balance position. Patients with the balance position shifted out of the dissected region (43%) presented the highest functional improvement after intervention; whereas those with the balance position shifted to the abdominal region (25%) showed unsatisfactory results. The magnitude of distal shifting of the first balance position at 3 months post intervention was statistically related to the subsequent true lumen expansion and false lumen reduction.

CONCLUSIONS

The first balance position of luminal pressure difference quantified the hemodynamic status of the dissected aorta. The magnitude of distal shifting of the balance position after intervention was associated with functional improvement and might be used predict longitudinal aortic remodeling.

Hemodialysis arterio-venous graft design reducing the hemodynamic risk of vascular access dysfunction

Although arterio-venous grafts (AVGs) represent the second choice as permanent vascular access for hemodialysis, this solution is still affected by a relevant failure rate due to graft thrombosis, and development of neointimal hyperplasia (IH) at the distal vein. As a key role in these processes has been attributed to the abnormal hemodynamics establishing in the distal vein, the optimization of AVGs design aimed at minimizing flow disturbances would reduce AVG hemodynamic-related risks. In this study we used computational fluid dynamics to investigate the impact of alternative AVG designs on the reduction of IH and thrombosis risk at the distal venous anastomosis. The performance of the newly designed AVGs was compared to that of commercially available devices. In detail, a total of eight AVG models in closed-loop configuration were constructed: two models resemble the commercially available straight conventional and helical-shaped AVGs; six models are characterized by the insertion of a flow divider (FD), straight or helical shaped, differently positioned inside the graft. Unfavorable hemodynamic conditions were analyzed by assessing the exposure to disturbed shear at the distal vein. Bulk flow was investigated in terms of helical blood flow features, potential thrombosis risk, and pressure drop over the graft. Findings from this study clearly show that using a helically-shaped FD located at the venous side of the graft could induce beneficial helical flow patterns that, minimizing flow disturbances, reduce the IH-related risk of failure at the distal vein, with a clinically irrelevant increase in thrombosis risk and pressure drop over the graft.

NUMERICAL INVESTIGATION OF THE EFFECTS OF BED SHAPE ON THE END-TO-SIDE CABG HEMODYNAMICS

Disrupted flow initiates and aggravates intimal thickening in the end-to-side (ETS) coronary artery bypass grafting (CABG), which may lead to failure. To enhance the post-intervention hemodynamics, the geometry is either optimized or totally reconfigured. Majority of configurations proposed by researchers have not suited CABG surgery, for they entailed rigorous manipulation on conventional grafts in situ, which was neither swift nor straightforward. The aim of the present study is, thus, to introduce a slight, yet effective, modification to a conventional ETS CABG configuration, and numerically investigate its effects on updated hemodynamic and structural environment, anticipating the longevity of proposed configuration and CABG success. This fairly simple modification may easily be made positioning a pre-designed anastomotic device between the bed of host artery in the conventional ETS CABG and its surrounding tissues. Conducting comprehensive numerical simulations, performance of the proposed configuration was assessed using idealized and patient-specific geometries of the conventional ETS CABG. Blood flow was simulated in a conventional and an updated CABG configuration considering 2-way fluid–structure interaction. Results revealed that, although the proposed configuration may induce higher structural stresses in vessels walls, it may improve important hemodynamic metrics such as wall shear stress gradient, oscillatory shear index, and relative residence time on host artery bed reducing disruption of flow. This study may also set the stage for design engineers and regulatory officials to evolve ETS CABG toward more hemodynamics-friendly approaches. Further in vitro, preclinical, and clinical experiments are, yet, entailed to accomplish ideal designs of procedural guidelines/grafts.

Efficiently Generating Mixing by Combining Differing Small Amplitude Helical Geometries

Helical geometries have been used in recent years to form cardiovascular prostheses such as stents and shunts. The helical geometry has been found to induce swirling flow, promoting in-plane mixing. This is hypothesised to reduce the formation of thrombosis and neo-intimal hyperplasia, in turn improving device patency and reducing re-implantation rates. In this paper we investigate whether joining together two helical geometries, of differing helical radii, in a repeating sequence, can produce significant gains in mixing effectiveness, by embodying a ‘streamline crossing’ flow environment. Since the computational cost of calculating particle trajectories over extended domains is high, in this work we devised a procedure for efficiently exploring the large parameter space of possible geometry combinations. Velocity fields for the single geometries were first obtained using the spectral/hp element method. These were then discontinuously concatenated, in series, for the particle tracking based mixing analysis of the combined geometry. Full computations of the most promising combined geometries were then performed. Mixing efficiency was evaluated quantitatively using Poincaré sections, particle residence time data, and information entropy. Excellent agreement was found between the idealised (concatenated flow field) and the full simulations of mixing performance, revealing that a strict discontinuity between velocity fields is not required for mixing enhancement, via streamline crossing, to occur. Optimal mixing was found to occur for the combination R = 0.2 D and R = 0.5 D , producing a 70 % increase in mixing, compared with standard single helical designs. The findings of this work point to the benefits of swirl disruption and suggest concatenation as an efficient means to determine optimal configurations of repeating geometries for future designs of vascular prostheses.

CFD and Optimization Study of Frictional Pressure Drop Through Bends

BACKGROUND

The non-Newtonian pseudoplastic liquid flow through different types of the bend is more complicated compared to the simple straight pipe as the bends are associated with various curve geometry. Bends have wide application in bioengineering, biotechnology and biomedical such as study biofluids, blood rheology study, the design of medical equipment like equipment measuring the cholesterol etc. Method: The papers deal with the estimation of loss coefficient and frictional pressure drop of Newtonian and non-Newtonian pseudoplastic fluid flow through the different bend of 0.0127 m diameter pipe geometry using commercially available CFD software fluent 6.3. We revised all patents relating to the pipe flow through different types of bend. The present study also deals with the efficient application of Genetic Algorithm (GA) for optimization of frictional pressure drop. Laminar Non-Newtonian Power law model is used for Sodium Carboxy Methyl Cellulose (SCMC) solution to solve the continuity and the momentum equations numerically. Generalized input-output correlation has been developed by Gene Expression Programming (GEP) using Matlab.

RESULTS

The above-mentioned algorithm is used to predict and optimize the pressure drop. It has been found that, the process exhibit the minimum pressure drop across the bend under optimum condition (Angle = 133.160, Concentration = 0.2 Kg/m3 and velocity = 0.53 m/s). The effect of flow rate, bend angle, fluid behaviour on static pressure and pressure drop has also been investigated.

CONCLUSION

From the study, it can be concluded that the developed GA model has a good agreement with the CFD model. The software predicted data might be used to solve various industrial problems and also to design different equipment.

Optimisation of a Novel Spiral-Inducing Bypass Graft Using Computational Fluid Dynamics

Graft failure is currently a major concern for medical practitioners in treating Peripheral Vascular Disease (PVD) and Coronary Artery Disease (CAD). It is now widely accepted that unfavourable haemodynamic conditions play an essential role in the formation and development of intimal hyperplasia, which is the main cause of graft failure. This paper uses Computational Fluid Dynamics (CFD) to conduct a parametric study to enhance the design and performance of a novel prosthetic graft, which utilises internal ridge(s) to induce spiral flow. This design is primarily based on the identification of the blood flow as spiral in the whole arterial system and is believed to improve the graft longevity and patency rates at distal graft anastomoses. Four different design parameters were assessed in this work and the trailing edge orientation of the ridge was identified as the most important parameter to induce physiological swirling flow, while the height of the ridge also significantly contributed to the enhanced performance of this type of graft. Building on these conclusions, an enhanced configuration of spiral graft is proposed and compared against conventional and spiral grafts to reaffirm its potential benefits.

Understanding the fluid mechanics behind transverse wall shear stress

The patchy distribution of atherosclerosis within arteries is widely attributed to local variation in haemodynamic wall shear stress (WSS). A recently-introduced metric, the transverse wall shear stress (transWSS), which is the average over the cardiac cycle of WSS components perpendicular to the temporal mean WSS vector, correlates particularly well with the pattern of lesions around aortic branch ostia. Here we use numerical methods to investigate the nature of the arterial flows captured by transWSS and the sensitivity of transWSS to inflow waveform and aortic geometry. TransWSS developed chiefly in the acceleration, peak systolic and deceleration phases of the cardiac cycle; the reverse flow phase was too short, and WSS in diastole was too low, for these periods to have a significant influence. Most of the spatial variation in transWSS arose from variation in the angle by which instantaneous WSS vectors deviated from the mean WSS vector rather than from variation in the magnitude of the vectors. The pattern of transWSS was insensitive to inflow waveform; only unphysiologically high Womersley numbers produced substantial changes. However, transWSS was sensitive to changes in geometry. The curvature of the arch and proximal descending aorta were responsible for the principal features, the non-planar nature of the aorta produced asymmetries in the location and position of streaks of high transWSS, and taper determined the persistence of the streaks down the aorta. These results reflect the importance of the fluctuating strength of Dean vortices in generating transWSS.

Numerical Assessment of Novel Helical/Spiral Grafts with Improved Hemodynamics for Distal Graft Anastomoses

In the present work, numerical simulations were conducted for a typical end-to-side distal graft anastomosis to assess the effects of inducing secondary flow, which is believed to remove unfavourable flow environment. Simulations were carried out for four models, generated based on two main features of 'out-of-plane helicity' and 'spiral ridge' in the grafts as well as their combination. Following a qualitative comparison against in vitro data, various mean flow and hemodynamic parameters were compared and the results showed that helicity is significantly more effective in inducing swirling flow in comparison to a spiral ridge, while their combination could be even more effective. In addition, the induced swirling flow was generally found to be increasing the wall shear stress and reducing the flow stagnation and particle residence time within the anastomotic region and the host artery, which may be beneficial to the graft longevity and patency rates. Finally, a parametric study on the spiral ridge geometrical features was conducted, which showed that the ridge height and the number of spiral ridges have significant effects on inducing swirling flow, and revealed the potential of improving the efficiency of such designs.

Haemodynamics and Flow Modification Stents for Peripheral Arterial Disease: A Review

Endovascular stents are widely used for the treatment of peripheral arterial disease (PAD). However, the development of in-stent restenosis and downstream PAD progression remain a challenge. Stent revascularisation of PAD causes arterial trauma and introduces abnormal haemodynamics, which initiate complicated biological processes detrimental to the arterial wall. The interaction between stent struts and arterial cells in contact, and the blood flow field created in a stented region, are highly affected by stent design. Spiral flow is known as a normal physiologic characteristic of arterial circulation and is believed to prevent the development of flow disturbances. This secondary flow motion is lost in atheromatous disease and its re-introduction after endovascular treatment of PAD has been suggested as a method to induce stabilised and coherent haemodynamics. Stent designs able to generate spiral flow may support endothelial function and therefore increase patency rates. This review is focused on secondary flow phenomena in arteries and the development of flow modification stent technologies for the treatment of PAD.

Effect of swirling blood flow on vortex formation at post-stenosis

Various clinical observations reported that swirling blood flow is a normal physiological flow pattern in various vasculatures. The swirling flow has beneficial effects on blood circulation through the blood vessels. It enhances oxygen transfer and reduces low-density lipoprotein concentration in the blood vessel by enhancing cross-plane mixing of the blood. However, the fluid-dynamic roles of the swirling flow are not yet fully understood. In this study, inhibition of material deposition at the post-stenosis region by the swirling flow was observed. To reveal the underlying fluid-dynamic characteristics, pathline flow visualization and time-resolved particle image velocimetry measurements were conducted. Results showed that the swirling inlet flow increased the development of vortices at near wall region of the post-stenosis, which can suppress further development of stenosis by enhancing transport and mixing of the blood flow. The fluid-dynamic characteristics obtained in this study would be useful for improving hemodynamic characteristics of vascular grafts and stents in which the stenosis frequently occurred. Moreover, the time-resolved particle image velocimetry measurement technique and vortex identification method employed in this study would be useful for investigating the fluid-dynamic effects of the swirling flow on various vascular environments.

Comparison of vortical structures induced by arteriovenous grafts using vector Doppler ultrasound

Arteriovenous prosthetic grafts are used in hemodialysis. Stenosis in the venous anastomosis is the main cause of occlusion and the role of local hemodynamics in this is considered significant. A new spiral graft design has been proposed to stabilize the flow phenomena in the host vein. Cross-flow vortical structures in the outflow of this graft were compared with those from a control device. Both grafts were integrated in identical in-house ultrasound-compatible flow phantoms with realistic surgical configurations. Constant flow rates were applied. In-plane 2-D velocity and vorticity mapping was developed using a vector Doppler technique. One or two vortices were detected for the spiral graft and two to four for the control, along with reduced stagnation points for the former. The in-plane peak velocity and circulation were calculated and found to be greater for the spiral device, implying increased in-plane mixing, which is believed to inhibit thrombosis and neo-intimal hyperplasia.

Fluid-dynamic optimal design of helical vascular graft for stenotic disturbed flow

Although a helical configuration of a prosthetic vascular graft appears to be clinically beneficial in suppressing thrombosis and intimal hyperplasia, an optimization of a helical design has yet to be achieved because of the lack of a detailed understanding on hemodynamic features in helical grafts and their fluid dynamic influences. In the present study, the swirling flow in a helical graft was hypothesized to have beneficial influences on a disturbed flow structure such as stenotic flow. The characteristics of swirling flows generated by helical tubes with various helical pitches and curvatures were investigated to prove the hypothesis. The fluid dynamic influences of these helical tubes on stenotic flow were quantitatively analysed by using a particle image velocimetry technique. Results showed that the swirling intensity and helicity of the swirling flow have a linear relation with a modified Germano number (Gn*) of the helical pipe. In addition, the swirling flow generated a beneficial flow structure at the stenosis by reducing the size of the recirculation flow under steady and pulsatile flow conditions. Therefore, the beneficial effects of a helical graft on the flow field can be estimated by using the magnitude of Gn*. Finally, an optimized helical design with a maximum Gn* was suggested for the future design of a vascular graft.

Coronary artery bypass grafting hemodynamics and anastomosis design: a biomedical engineering review

In this paper, coronary arterial bypass grafting hemodynamics and anastomosis designs are reviewed. The paper specifically addresses the biomechanical factors for enhancement of the patency of coronary artery bypass grafts (CABGs). Stenosis of distal anastomosis, caused by thrombosis and intimal hyperplasia (IH), is the major cause of failure of CABGs. Strong correlations have been established between the hemodynamics and vessel wall biomechanical factors and the initiation and development of IH and thrombus formation. Accordingly, several investigations have been conducted and numerous anastomotic geometries and devices have been designed to better regulate the blood flow fields and distribution of hemodynamic parameters and biomechanical factors at the distal anastomosis, in order to enhance the patency of CABGs. Enhancement of longevity and patency rate of CABGs can eliminate the need for re-operation and can significantly lower morbidity, and thereby reduces medical costs for patients suffering from coronary stenosis. This invited review focuses on various endeavors made thus far to design a patency-enhancing optimized anastomotic configuration for the distal junction of CABGs.

Numerical Simulation of Physiological Blood Flow in 2-way Coronary Artery Bypass Grafts

The Coronary Artery Bypass Graft (CABG) yields excellent results and remains the modern standard of care for treatment of occlusive disease in the cardiovascular system. However, the development of anastomotic Intimal Hyperplasia (IH) and restenosis can compromise the medium-and-long term effects of the CABG. This problem can be correlated with the geometric configuration and hemodynamics of the bypass graft. A novel geometric configuration was proposed for the CABG with two symmetrically implanted grafts for the purpose of improving the hemodynamics. Physiological blood flows in two models of bypass grafts were simulated using numerical methods. One model was for the conventional bypass configuration with a single graft (1-way model); the other model was for the proposed bypass configuration with two grafts (2-way model). The temporal and spatial distributions of hemodynamics, such as flow patterns and Wall Shear Stress (WSS) in the vicinity of the distal anastomoses, were analyzed and compared. Calculation results showed that the 2-way model possessed favorable hemodynamics with uniform longitudinal flow patterns and WSS distributions, which could decrease the probability of restenosis and improve the effect of the surgical treatment. Concerning the limitations of the 2-way bypass grafts, it is necessary to perform animal experiments to verify the viability of this novel idea for the CABG.

A computational exploration of helical arterio-venous graft designs

Although arterio-venous grafts (AVGs) are the second best option as long-term vascular access for hemodialysis, they suffer from complications caused by intimal hyperplasia, mainly located in vessel regions of low and oscillating wall shear stress. However, certain flow patterns in the bulk may reduce these unfavorable hemodynamic conditions. We therefore studied, with computational fluid dynamics (CFD), the impact of a helical AVG design on the occurrence of (un)favorable hemodynamic conditions at the venous anastomosis. Six CFD-models of an AVG in closed-loop configuration were constructed: one conventional straight graft, and five helical designed grafts with a pitch of 105 mm down to 35 mm. At the venous anastomosis, disturbed shear was assessed by quantifying the area with unfavorable conditions, and by analyzing averaged values in a case-specific patch. The bulk hemodynamics were assessed by analyzing the kinetic helicity in and the pressure drop over the graft. The most helical design scores best, being instrumental to suppress disturbed shear in the venous segment. There is, however, no trivial relationship between the number of helix turns of the graft and disturbed shear in the venous segment, when a realistic closed-loop AVG model is investigated. Bulk flow investigation showed a marked increase of helicity intensity in, and a moderate pressure drop over the AVG by introducing a lower pitch. At the venous anastomosis, unfavorable hemodynamic conditions can be reduced by introducing a helical design. However, due to the complex flow conditions, the optimal helical design for an AVG cannot be derived without studying case by case.

Numerical analysis of coronary artery bypass grafts: an over view

Arterial bypass grafts tend to fail after some years due to the development of intimal thickening (restenosis). Non-uniform hemodynamics following a bypass operation contributes to restenosis and bypass failure can occur due to the focal development of anastomotic intimal hyperplasia. Additionally, surgical injury aggravated by compliance mismatch between the graft and artery has been suggested as an initiating factor for progress of wall thickening along the suture line Vascular grafts that are small in diameter tend to occlude rapidly. Computational fluid dynamics (CFD) methods have been effectively used to simulate the physical and geometrical parameters characterizing the hemodynamics of various arteries and bypass configurations. The effects of such changes on the pressure and flow characteristics as well as the wall shear stress during a cardiac cycle can be simulated. Recently, utilization of fluid and structure interactions have been used to determine fluid flow parameters and structure forces including stress and strains relationships under steady and transient conditions. In parallel to this, experimental diagnostics techniques such as Laser Doppler Anemometry, Particle Image Velocimetry, Doppler Guide wire and Magnetic Resonance Imaging have been used to provide essential information and to validate the numerical results. Moreover, clinical imaging techniques such as magnetic resonance or computed tomography have assisted considerably in gaining a detailed patient-specific picture of the blood flow and structure dynamics. This paper gives a review of recent numerical investigations of various configurations of coronary artery bypass grafts (CABG). In addition, the paper ends with a summary of the findings and the future directions.

Haemodynamics in the mouse aortic arch computed from MRI-derived velocities at the aortic root

Mice are widely used to investigate atherogenesis, which is known to be influenced by stresses related to blood flow. However, numerical characterization of the haemodynamic environment in the commonly studied aortic arch has hitherto been based on idealizations of inflow into the aorta. Our purpose in this work was to numerically characterize the haemodynamic environment in the mouse aortic arch using measured inflow velocities, and to relate the resulting shear stress patterns to known locations of high- and low-lesion prevalence. Blood flow velocities were measured in the aortic root of C57/BL6 mice using phase-contrast MRI. Arterial geometries were obtained by micro-CT of corrosion casts. These data were used to compute blood flow and wall shear stress (WSS) patterns in the arch. WSS profiles computed using realistic and idealized aortic root velocities differed significantly. An unexpected finding was that average WSS in the high-lesion-probability region on the inner wall was actually higher than the WSS in the low-probability region on the outer wall. Future studies of mouse aortic arch haemodynamics should avoid the use of idealized inflow velocity profiles. Lesion formation does not seem to uniquely associate with low or oscillating WSS in this segment, suggesting that other factors may also play a role in lesion localization.

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.

Effect of reverse flow on the pattern of wall shear stress near arterial branches

Atherosclerotic lesions have a patchy distribution within arteries that suggests a controlling influence of haemodynamic stresses on their development. The distribution near aortic branches varies with age and species, perhaps reflecting differences in these stresses. Our previous work, which assumed steady flow, revealed a dependence of wall shear stress (WSS) patterns on Reynolds number and side-branch flow rate. Here, we examine effects of pulsatile flow. Flow and WSS patterns were computed by applying high-order unstructured spectral/hp element methods to the Newtonian incompressible Navier-Stokes equations in a geometrically simplified model of an aorto-intercostal junction. The effect of pulsatile but non-reversing side-branch flow was small; the aortic WSS pattern resembled that obtained under steady flow conditions, with high WSS upstream and downstream of the branch. When flow in the side branch or in the aortic near-wall region reversed during part of the cycle, significantly different instantaneous patterns were generated, with low WSS appearing upstream and downstream. Time-averaged WSS was similar to the steady flow case, reflecting the short duration of these events, but patterns of the oscillatory shear index for reversing aortic near-wall flow were profoundly altered. Effects of reverse flow may help explain the different distributions of lesions.

Computer-Aided Patient-Specific Coronary Artery Graft Design Improvements Using CFD Coupled Shape Optimizer

This study aims to (i) demonstrate the efficacy of a new surgical planning framework for complex cardiovascular reconstructions, (ii) develop a computational fluid dynamics (CFD) coupled multi-dimensional shape optimization method to aid patient-specific coronary artery by-pass graft (CABG) design and, (iii) compare the hemodynamic efficiency of the sequential CABG, i.e., raising a daughter parallel branch from the parent CABG in patient-specific 3D settings. Hemodynamic efficiency of patient-specific complete revascularization scenarios for right coronary artery (RCA), left anterior descending artery (LAD), and left circumflex artery (LCX) bypasses were investigated in comparison to the stenosis condition. Multivariate 2D constraint optimization was applied on the left internal mammary artery (LIMA) graft, which was parameterized based on actual surgical settings extracted from 2D CT slices. The objective function was set to minimize the local variation of wall shear stress (WSS) and other hemodynamic indices (energy dissipation, flow deviation angle, average WSS, and vorticity) that correlate with performance of the graft and risk of re-stenosis at the anastomosis zone. Once the optimized 2D graft shape was obtained, it was translated to 3D using an in-house "sketch-based" interactive anatomical editing tool. The final graft design was evaluated using an experimentally validated second-order non-Newtonian CFD solver incorporating resistance based outlet boundary conditions. 3D patient-specific simulations for the healthy coronary anatomy produced realistic coronary flows. All revascularization techniques restored coronary perfusions to the healthy baseline. Multi-scale evaluation of the optimized LIMA graft enabled significant wall shear stress gradient (WSSG) relief (~34%). In comparison to original LIMA graft, sequential graft also lowered the WSSG by 15% proximal to LAD and diagonal bifurcation. The proposed sketch-based surgical planning paradigm evaluated the selected coronary bypass surgery procedures based on acute hemodynamic readjustments of aorta-CA flow. This methodology may provide a rational to aid surgical decision making in time-critical, patient-specific CA bypass operations before in vivo execution.

Hemodynamics of an end-to-side anastomotic graft for a pulsatile pediatric ventricular assist device

Numerical simulations are performed to investigate the flow within the end-to-side proximal anastomosis of a pulsatile pediatric ventricular assist device (PVAD) to an aorta. The anastomotic model is constructed from a patient-specific pediatric aorta. The three great vessels originating from the aortic arch--brachiocephalic (innominate), left common carotid, and left subclavian arteries--are included. An implicit large eddy simulation method based on a finite volume approach is used to study the resulting turbulent flow. A resistance boundary condition is applied at each branch outlet to study flow splitting. The PVAD anastomosis is found to alter the aortic flow dramatically. More flow is diverted into the great vessels with the PVAD support. Turbulence is found in the jet impingement area at peak systole for 100% bypass, and a maximum principal normal Reynolds stress of 7081 dyn/cm(2) is estimated based on ten flow cycles. This may be high enough to cause hemolysis and platelet activation. Regions prone to intimal hyperplasia are identified by combining the time-averaged wall shear stress and oscillatory shear index. These regions are found to vary, depending on the percentage of the flow bypass.

Flow instability and wall shear stress variation in intracranial aneurysms

We investigate the flow dynamics and oscillatory behaviour of wall shear stress (WSS) vectors in intracranial aneurysms using high resolution numerical simulations. We analyse three representative patient-specific internal carotid arteries laden with aneurysms of different characteristics: (i) a wide-necked saccular aneurysm, (ii) a narrower-necked saccular aneurysm, and (iii) a case with two adjacent saccular aneurysms. Our simulations show that the pulsatile flow in aneurysms can be subject to a hydrodynamic instability during the decelerating systolic phase resulting in a high-frequency oscillation in the range of 20-50 Hz, even when the blood flow rate in the parent vessel is as low as 150 and 250 ml min(-1) for cases (iii) and (i), respectively. The flow returns to its original laminar pulsatile state near the end of diastole. When the aneurysmal flow becomes unstable, both the magnitude and the directions of WSS vectors fluctuate at the aforementioned high frequencies. In particular, the WSS vectors around the flow impingement region exhibit significant spatio-temporal changes in direction as well as in magnitude.

Numerical Study of Blood Flow at the End-to-Side Anastomosis of a Left Ventricular Assist Device for Adult Patients

We use an implicit large eddy simulation (ILES) method based on a finite volume approach to capture the turbulence in the anastomoses of a left ventricular assist device (LVAD) to the aorta. The order-of-accuracy of the numerical schemes is computed using a two-dimensional decaying Taylor–Green vortex. The ILES method is carefully validated by comparing to documented results for a fully developed turbulent channel flow at Reτ=395. Two different anastomotic flows (proximal and distal) are simulated for 50% and 100% LVAD supports and the results are compared with a healthy aortic flow. All the analyses are based on a planar aortic model under steady inflow conditions for simplification. Our results reveal that the outflow cannulae induce high exit jet flows in the aorta, resulting in turbulent flow. The distal configuration causes more turbulence in the aorta than the proximal configuration. The turbulence, however, may not cause any hemolysis due to low Reynolds stresses and relatively large Kolmogorov length scales compared with red blood cells. The LVAD support causes an acute increase in flow splitting in the major branch vessels for both anastomotic configurations, although its long-term effect on the flow splitting remains unknown. A large increase in wall shear stress is found near the cannulation sites during the LVAD support. This work builds a foundation for more physiologically realistic simulations under pulsatile flow conditions.

Wall shear stress and pressure distribution on aneurysms and infundibulae in the posterior communicating artery bifurcation

A growing number of cases of rupture at an infundibulum, progression of infundibulum to a frank aneurysm, and subarachnoid hemorrhage (SAH) in the posterior communicating artery (PCoA) have been reported. Using patient-specific geometric models of the supraclinoid internal carotid artery (ICA) with PCoA infundibulum or aneurysm, high-resolution computational fluid dynamics simulations were performed by solving the Navier-Stokes equations with a spectral/hp element method. Simulation results show that the flow impinges at the distal wall of infundibulum near the outside of the ICA bend and creates a region of higher pressure (4-5 mmHg) surrounded by a band of a high wall shear stress (WSS) (20-30 N/m(2) on average). At the proximal end of the infundibulum, another stagnation area is formed characterized by low WSS (<1 N/m(2)) and high oscillating shear index. This impingement region seems to coincide with the locations of the rupture of infundibulae or progression to aneurysms. In addition, the pulsatile flow becomes unstable due to the presence of aneurysms or aneurysm-like infundibulae, and this leads to WSS temporal fluctuations inside the aneurysm, which may accelerate the degenerative processes in the vessel walls.

A framework for geometric analysis of vascular structures: application to cerebral aneurysms

There is well-documented evidence that vascular geometry has a major impact in blood flow dynamics and consequently in the development of vascular diseases, like atherosclerosis and cerebral aneurysmal disease. The study of vascular geometry and the identification of geometric features associated with a specific pathological condition can therefore shed light into the mechanisms involved in the pathogenesis and progression of the disease. Although the development of medical imaging technologies is providing increasing amounts of data on the three-dimensional morphology of the in vivo vasculature, robust and objective tools for quantitative analysis of vascular geometry are still lacking. In this paper, we present a framework for the geometric analysis of vascular structures, in particular for the quantification of the geometric relationships between the elements of a vascular network based on the definition of centerlines. The framework is founded upon solid computational geometry criteria, which confer robustness of the analysis with respect to the high variability of in vivo vascular geometry. The techniques presented are readily available as part of the VMTK, an open source framework for image segmentation, geometric characterization, mesh generation and computational hemodynamics specifically developed for the analysis of vascular structures. As part of the Aneurisk project, we present the application of the present framework to the characterization of the geometric relationships between cerebral aneurysms and their parent vasculature.

Effect of Reynolds number and flow division on patterns of haemodynamic wall shear stress near branch points in the descending thoracic aorta

Atherosclerotic lesions are non-uniformly distributed at arterial bends and branch sites, suggesting an important role for haemodynamic factors, particularly wall shear stress (WSS), in their development. The pattern of lesions at aortic branch sites depends on age and species. Using computational flow simulations in an idealized model of an intercostal artery emerging perpendicularly from the thoracic aorta, we studied the effects of Reynolds number and flow division under steady conditions. Patterns of flow and WSS were strikingly dependent on these haemodynamic parameters. With increasing Reynolds number, WSS, normalized by the fully developed aortic value, was lowered at the sides of the ostium and increased upstream and downstream of it. Increasing flow into the side branch exacerbated these patterns and gave rise to a reversing flow region downstream of the ostium. Incorporation of more realistic geometric features had only minor effects and patterns of mean WSS under pulsatile conditions were similar to the steady flow results. Aspects of the observed WSS patterns correlate with, and may explain, some but not all of the lesion patterns in human, rabbit and mouse aortas.

Rheological Effects of Blood in a Nonplanar Distal End-to-Side Anastomosis

This study investigates rheological effects of blood on steady flows in a nonplanar distal end-to-side anastomosis. The shear-thinning behavior of blood is depicted by a Carreau–Yasuda model and a modified power-law model. To explore effects of nonplanarity in vessel geometry, a curved bypass graft is considered that connects to the host artery with a 90deg out-of-plane curvature. Navier–Stokes equations are solved using a finite volume method. Velocity and wall shear stress (WSS) are compared between Newtonian and non-Newtonian fluids at different flow rates. At low flow rate, difference in axial velocity profiles between Newtonian and non-Newtonian fluids is significant and secondary flows are weaker for non-Newtonian fluids. At high flow rate, non-Newtonian fluids have bigger peak WSS and WSS gradient. The size of the flow recirculation zone near the toe is smaller for non-Newtonian fluids and the difference is significant at low flow rate. The nonplanar bypass graft introduces helical flow in the host vessel. Results from the study reveal that near the bed, heel, and toe of the anastomotic junction where intimal hyperplasia occurs preferentially, WSS gradients are all very big. At high flow rates, WSS gradients are elevated by the non-Newtonian effect of blood but they are reduced at low flow rates. At these locations, blood rheology not only affects the WSS and its gradient but also secondary flow patterns and the size of flow recirculation near the toe. This study reemphasizes that the rheological property of blood is a key factor in studying hemodynamic effects on vascular diseases.

A parametric model for studies of flow in arterial bifurcations

Regional differences in hemodynamic loads on arterial walls have been associated with localized vascular disease such as atherosclerosis and cerebral aneurysms. Due to their intrinsic geometric relevance, three-dimensional (3D) reconstructions of arterial segments are frequently used in hemodynamic studies of these diseases. However, it is not possible to use them to systematically vary geometric features for parametric studies. Idealized vascular models are inherently suited for parametric studies, but are limited by their tendency to oversimplify the vessel geometry. In this work, a hierarchy of three parametric bifurcation models is introduced. The models are relatively simple, yet capture all geometric features identified as common to cerebral bifurcations in the complex transition from parent to daughter branches. While these models were initially designed for parametric studies, we also evaluate the possibility of using them for 3D reconstruction of cerebral arteries, with the future goal of improving reconstruction of poor quality clinical data. The lumen surface and vessel hemodynamics are compared between two reconstructed cerebral bifurcations and matched parametric models. Good agreement is found. The average and maximum geometric differences are less than 3.1 and 10%, respectively for all three parametric models. The maximum difference in wall shear stress is less than 8% for the most complex parametric model.

Flow and wall shear stress in end-to-side and side-to-side anastomosis of venous coronary artery bypass grafts

PURPOSE

Coronary artery bypass graft (CABG) surgery represents the standard treatment of advanced coronary artery disease. Two major types of anastomosis exist to connect the graft to the coronary artery, i.e., by using an end-to-side or a side-to-side anastomosis. There is still controversy because of the differences in the patency rates of the two types of anastomosis. The purpose of this paper is to non-invasively quantify hemodynamic parameters, such as mass flow and wall shear stress (WSS), in end-to-side and side-to-side anastomoses of patients with CABG using computational fluid dynamics (CFD).

METHODS

One patient with saphenous CABG and end-to-side anastomosis and one patient with saphenous CABG and side-to-side anastomosis underwent 16-detector row computed tomography (CT). Geometric models of coronary arteries and bypasses were reconstructed for CFD analysis. Blood flow was considered pulsatile, laminar, incompressible and Newtonian. Peri-anastomotic mass flow and WSS were quantified and flow patterns visualized.

RESULTS

CFD analysis based on in-vivo CT coronary angiography data was feasible in both patients. For both types of CABG, flow patterns were characterized by a retrograde flow into the native coronary artery. WSS variations were found in both anastomoses types, with highest WSS values at the heel and lowest WSS values at the floor of the end-to-side anastomosis. In contrast, the highest WSS values of the side-to-side anastomosis configuration were found in stenotic vessel segments and not in the close vicinity of the anastomosis. Flow stagnation zones were found in end-to-side but not in side-to-side anastomosis, the latter also demonstrating a smoother stream division throughout the cardiac cycle.

CONCLUSION

CFD analysis of venous CABG based on in-vivo CT datasets in patients was feasible producing qualitative and quantitative information on mass flow and WSS. Differences were found between the two types of anastomosis warranting further systematic application of the presented methodology on multiple patient datasets.

A Helical PTFE Arteriovenous Access Graft to Swirl Flow Across the Distal Anastomosis: Results of a Preliminary Clinical Study

Intimal hyperplasia develops preferentially in regions where the blood flow is stagnant and wall shear stress low. The small amplitude helical geometry of the SwirlGraft was designed to ensure physiological-type swirling flow, and thus suppress the triggers. We report the first conceptual testing of the SwirlGraft. Primary, assisted primary and secondary patency rates at 6 months in 20 patients were 57.9+/-11.4%, 84.4+/-8.3% and 100+/-0.0%. There was angiographic evidence of reduction of helical geometry in a proportion of the grafts. The helical graft is associated with high assisted primary and secondary patency. Elaboration of the surgical implantation techniques and an improved SwirlGraft design can be expected to exploit the advantages of the helical concept.

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.

Haemodynamics and wall remodelling of a growing cerebral aneurysm: A computational model

We have developed a computational simulation model for investigating an often postulated hypothesis connected with aneurysm growth. This hypothesis involves a combination of two parallel and interconnected mechanisms: according to the first mechanism, an endothelium-originating and wall shear stress-driven apoptotic behavior of smooth muscle cells, leading to loss of vascular tone is believed to be important to the aneurysm behavior. Vascular tone refers to the degree of constriction experienced by a blood vessel relative to its maximally dilated state. All resistance and capacitance vessels under basal conditions exhibit some degree of smooth muscle contraction that determines the diameter, and hence tone, of the vessel. The second mechanism is connected to the arterial wall remodeling. Remodeling of the arterial wall under constant tension is a biomechanical process of rupture, degradation and reconstruction of the medial elastin and collagen fibers. In order to investigate these two mechanisms within a computationally tractable framework, we devise mechanical analogues that involve three-dimensional haemodynamics, yielding estimates of the wall shear stress and pressure fields and a quasi-steady approach for the apoptosis and remodeling of the wall. These analogues are guided by experimental information for the connection of stimuli to responses at a cellular level, properly averaged over volumes or surfaces. The model predicts aneurysm growth and can attribute specific roles to the two mechanisms involved: the smooth muscle cell-related loss of tone is important to the initiation of aneurysm growth, but cannot account alone for the formation of fully grown sacks; the fiber-related remodeling is pivotal for the latter.

Preliminary comparative study of small amplitude helical and conventional ePTFE arteriovenous shunts in pigs

Intimal hyperplasia (IH), which causes occlusion of arterial bypass grafts and arteriovenous (A-V) shunts, develops preferentially in low wall shear, or stagnation, regions. Arterial geometry is commonly three-dimensional, generating swirling flows, the characteristics of which include in-plane mixing and inhibition of stagnation. Clinical arterial bypass grafts are commonly two-dimensional, favouring extremes of wall shear. We have developed small amplitude helical technology (SwirlGraft) devices and shown them to generate physiological-type swirling flows. Expanded polytetrafluorethylene (ePTFE) grafts, although widely used as A-V shunts for renal dialysis access, are prone to thrombosis and IH. In a small preliminary study in pigs, we have implanted SwirlGraft ePTFE carotid artery-to-jugular vein shunts on one side and conventional ePTFE carotid artery-to-jugular vein shunts contralaterally. There was consistently less thrombosis and IH in the SwirlGraft than conventional shunts. At eight weeks (two animals), the differences were marked, with virtually no disease in the SwirlGraft devices and occlusion of the conventional grafts by thrombosis and IH. The study had limitations, but the lesser pathology in the SwirlGraft devices is likely to have resulted from their geometry and the associated swirling flow. The results could have implications for vascular biology and prolongation of the patency of arterial bypass grafts and A-V shunts.

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.

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.

Fluid flow structure in arterial bypass anastomosis

The fluid flow through a stenosed artery and its bypass graft in an anastomosis can substantially influence the outcome of bypass surgery. To help improve our understanding of this and related issues, the steady Navier-Stokes flows are computed in an idealized arterial bypass system with partially occluded host artery. Both the residual flow issued from the stenosis--which is potentially important at an earlier stage after grafting--and the complex flow structure induced by the bypass graft are investigated. Seven geometric models, including symmetric and asymmetric stenoses in the host artery, and two major aspects of the bypass system, namely, the effects of area reduction and stenosis asymmetry, are considered. By analyzing the flow characteristics in these configurations, it is found that (1) substantial area reduction leads to flow recirculation in both upstream and downstream of the stenosis and in the host artery near the toe, while diminishes the recirculation zone in the bypass graft near the bifurcation junction, (2) the asymmetry and position of the stenosis can affect the location and size of these recirculation zones, and (3) the curvature of the bypass graft can modify the fluid flow structure in the entire bypass system.

Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model

A three-dimensional model with simplified geometry for the branched coronary artery is presented. The bifurcation is defined by an analytical intersection of two cylindrical tubes lying on a sphere that represents an idealized heart surface. The model takes into account the repetitive variation of curvature and motion to which the vessel is subject during each cardiac cycle, and also includes the phase difference between arterial motion and blood flowrate, which may be nonzero for patients with pathologies such as aortic regurgitation. An arbitrary Lagrangian Eulerian (ALE) formulation of the unsteady, incompressible, three-dimensional Navier-Stokes equations is employed to solve for the flow field, and numerical simulations are performed using the spectral/hp element method. The results indicate that the combined effect of pulsatile inflow and dynamic geometry depends strongly on the aforementioned phase difference. Specifically, the main findings of this work show that the time-variation of flowrate ratio between the two branches is minimal (less than 5%) for the simulation with phase difference angle equal to 90 degrees, and maximal (51%) for 270 degrees. In two flow pulsatile simulation cases for fixed geometry and dynamic geometry with phase angle 270 degrees, there is a local minimum of the normalized wall shear rate amplitude in the vicinity of the bifurcation, while in other simulations a local maximum is observed.

Computational modeling of vascular anastomoses

Recent development of computational technology allows a level of knowledge of biomechanical factors in the healthy or pathological cardiovascular system that was unthinkable a few years ago. In particular, computational fluid dynamics (CFD) and computational structural (CS) analyses have been used to evaluate specific quantities, such as fluid and wall stresses and strains, which are very difficult to measure in vivo. Indeed, CFD and CS offer much more variability and resolution than in vitro and in vivo methods, yet computations must be validated by careful comparison with experimental and clinical data. The enormous parallel development of clinical imaging such as magnetic resonance or computed tomography opens a new way toward a detailed patient-specific description of the actual hemodynamics and structural behavior of living tissues. Coupling of CFD/CS and clinical images is becoming a standard evaluation that is expected to become part of the clinical practice in the diagnosis and in the surgical planning in advanced medical centers. This review focuses on computational studies of fluid and structural dynamics of a number of vascular anastomoses: the coronary bypass graft anastomoses, the arterial peripheral anastomoses, the arterio-venous graft anastomoses and the vascular anastomoses performed in the correction of congenital heart diseases.

Automated classification of peripheral distal by-pass geometries reconstructed from medical data

Abnormal haemodynamic conditions are implicated in the development of anastomotic myointimal hyperplasia (MIH). However, these conditions are difficult to determine in vivo, prompting research using ex vivo idealised models. To relate the understanding gained in idealised geometries to anatomically correct conditions we have investigated a reproducible approach to classify in vivo distal graft anastomoses and their inter-patient variability. In vivo distal anastomotic geometries were acquired by magnetic resonance (MR) angiography from 13 patients who had undergone infrageniculate autologous venous by-pass surgery. On average, the images were acquired 2 weeks post-operatively. Five patients also underwent repeat examinations 2 to 7 weeks later. For each geometry, the surface of the arterial lumen is represented by the zero level set of an implicit function constructed from radial basis functions that minimise curvature. The three-dimensional binary image created from the interpolated surface is processed using a skeletonisation algorithm to obtain the centreline of each branch in the geometry. This allows for the measurement of the branching angles between straight line approximations of the centrelines of each vessel, averaging them over a characteristic length of each anastomosis. The main finding in the application of the proposed classification methodology to this set of patients is that the spectrum of anastomoses can be reduced to a small subset of cases characterised by two angles: the angle between the graft and the plane of the host artery and the angle between the graft and the proximal branch of the artery.

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier-Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau-Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.

Three-dimensional reconstruction of autologous vein bypass graft distal anastomoses imaged with magnetic resonance: clinical and research applications

High-resolution magnetic resonance imaging was combined with computational modeling to create focused three-dimensional reconstructions of the distal anastomotic region of autologous vein peripheral bypass grafts in a preliminary series of patients. Readily viewed on a personal computer or printed as hard copies, a detailed appreciation of in vivo postoperative features of the anastomosis is possible. These reconstructions are suitable for analysis of geometric features, including vessel caliber, tortuosity, anastomotic angles, and planarity. Some potential clinical and research applications of this technique are discussed.