A numerical simulation of flow in a two-dimensional end-to-side anastomosis model

Computational model-based hemodynamic comparisons of traditional and modified idealized models of autologous radiocephalic fistula

Autologous arteriovenous fistula (AVF) is a commonly used vascular access (VA) for hemodialysis, and hemodynamic changes are one of the main factors for its failure. To explore the effect of geometry on the hemodynamics in the AVF, a modified model is built with a gradual and smooth turn at the anastomosis and is compared with the traditional model, which has an abrupt sharp turn at the anastomisis. Transient computational fluid dynamics (CFD) simulations were performed for the comparison and analysis of the hemodynamic fields of the two models at different stages of the pulse cycle. The results showed that the low shear stress region and high oscillatory shear stress region in the modified AVF model coincided with regions of intimal hyperplasia that have been identified by previous studies. A comparison with the blood flow velocities measured in vivo was performed, and the error between the simulation results and the medical data was reduced by 22% in the modified model, which verifies the rationality and utility of the modified model.

Literature Survey for In-Vivo Reynolds and Womersley Numbers of Various Arteries and Implications for Compliant In-Vitro Modelling

PURPOSE

In-vitro modelling can be used to investigate haemodynamics of arterial geometry and stent implants. However, in-vitro model fidelity relies on precise matching of in-vivo conditions. In pulsatile flow, velocity distribution and wall shear stress depend on compliance, and the Reynolds and Womersley numbers. However, matching such values may lead to unachievable tolerances in phantom fabrication.

METHODS

Published Reynolds and Womersley numbers for 14 major arteries in the human body were determined via a literature search. Preference was given to in-vivo publications but in-vitro and in-silico values were presented when in-vivo values were not found. Subsequently ascending aorta and carotid artery case studies were presented to highlight the limitations dynamic matching would apply to phantom fabrication.

RESULTS

Seven studies reported the in-vivo Reynolds and Womersley numbers for the aorta and two for the carotid artery. However, only one study each reported in-vivo numbers for the remaining ten arteries. No in-vivo data could be found for the femoral, superior mesenteric and renal arteries. Thus, information derived in-vitro and in-silico were provided instead. The ascending aorta and carotid artery models required scaling to 1.5× and 3× life-scale, respectively, to achieve dimensional tolerance restrictions. Modelling the ascending aorta with the comparatively high viscosity water/glycerine solution will lead to high pump power demands. However, all the working fluids considered could be dynamically matched with low pump demand for the carotid model.

CONCLUSION

This paper compiles available human haemodynamic information, and highlights the paucity of information for some arteries. It also provides a method for optimal in-vitro experimental configuration.

Hemodynamics and Wall Mechanics of Vascular Graft Failure

Blood vessels are subjected to complex biomechanical loads, primarily from pressure-driven blood flow. Abnormal loading associated with vascular grafts, arising from altered hemodynamics or wall mechanics, can cause acute and progressive vascular failure and end-organ dysfunction. Perturbations to mechanobiological stimuli experienced by vascular cells contribute to remodeling of the vascular wall via activation of mechanosensitive signaling pathways and subsequent changes in gene expression and associated turnover of cells and extracellular matrix. In this review, we outline experimental and computational tools used to quantify metrics of biomechanical loading in vascular grafts and highlight those that show potential in predicting graft failure for diverse disease contexts. We include metrics derived from both fluid and solid mechanics that drive feedback loops between mechanobiological processes and changes in the biomechanical state that govern the natural history of vascular grafts. As illustrative examples, we consider application-specific coronary artery bypass grafts, peripheral vascular grafts, and tissue-engineered vascular grafts for congenital heart surgery as each of these involves unique circulatory environments, loading magnitudes, and graft materials.

End-to-side Anastomosis on Digital Arteries: Just a Technical Choice or a Real Benefit?

High-quality evidence is currently poor regarding the benefits of end-to-end (ETE) or end-to-side (ETS) anastomosis in arterial and venous anastomoses, despite being postulated as a potential influence on outcomes. A sufficient microvascular anastomosis is indispensable for the success of any free tissue transfer. ETS microvascular anastomoses have been becoming increasingly important as they allow reconstruction even in patients with impaired vascular status. To the authors’ knowledge, no studies have examined the choice of ETE or ETS anastomoses specifically for digital arteries.

Biomechanics and Mechanobiology of Saphenous Vein Grafts

Within several weeks of use as coronary artery bypass grafts (CABG), saphenous veins (SV) exhibit significant intimal hyperplasia (IH). IH predisposes vessels to thrombosis and atherosclerosis, the two major modes of vein graft failure. The fact that SV do not develop significant IH in their native venous environment coupled with the rapidity with which they develop IH following grafting into the arterial circulation suggests that factors associated with the isolation and preparation of SV and/or differences between the venous and arterial environments contribute to disease progression. There is strong evidence suggesting that mechanical trauma associated with traditional techniques of SV preparation can significantly damage the vessel and might potentially reduce graft patency though modern surgical techniques reduces these injuries. In contrast, it seems possible that modern surgical technique, specifically endoscopic vein harvest, might introduce other mechanical trauma that could subtly injure the vein and perhaps contribute to the reduced patency observed in veins harvested using endoscopic techniques. Aspects of the arterial mechanical environment influence remodeling of SV grafted into the arterial circulation. Increased pressure likely leads to thickening of the medial wall but its role in IH is less clear. Changes in fluid flow, including increased average wall shear stress, may reduce IH while disturbed flow likely increase IH. Nonmechanical stimuli, such as exposure to arterial levels of oxygen, may also have a significant but not widely recognized role in IH. Several potentially promising approaches to alter the mechanical environment to improve graft patency are including extravascular supports or altered graft geometries are covered.

THE INFLUENCE OF USING THE NEEDLE ADAPTER TO REDUCE THE BIOMECHANICAL RISK FACTORS WITHIN HEMODIALYSIS ARTERIOVENOUS GRAFTS

Hemodialysis vascular access failure is related to increased morbidity and mortality in hemodialysis patients, representing a challenging clinical problem which results in a high percentage of hospital entrance and an important economic burden on government's disbursement. In this paper, the feasibility of using the needle adapter to reduce the biomechanical risk factors within arteriovenous grafts is considered. The three-dimensional (3D) tapered 6 to 8 mm loop graft in the presence of venous and arterial needles with and without adapter was numerically simulated. Navier–Stokes equations for incompressible Newtonian fluid are the governing equation of this problem. k – ω two equations turbulence modeling were applied to capture flow features of low Reynolds turbulent flow regions in this simulation. The physiological velocity waveform was used as an arterial inlet boundary condition. The venose outlet boundary condition was a time dependent physiological pressure waveform. The results for the dialysis without the adapter demonstrated that the graft wall experiences increased hemodynamic stresses as a result of the hitting needle jet flow. The dialysis with the adapter demonstrated that the venous anastomosis experiences lower biomechanical risk factors in comparison to the dialysis without the adapter and it reduced the vascular access failure. Using adapter caused less damage to endothelial cells during hemodialysis.

Disturbed flow in radial-cephalic arteriovenous fistulae for haemodialysis: low and oscillating shear stress locates the sites of stenosis

BACKGROUND

Despite recent clinical and technological advancements, the vascular access (VA) for haemodialysis still has significant early failure rates after arteriovenous fistula (AVF) creation. VA failure is mainly related to the haemodynamic conditions that trigger the phenomena of vascular wall disease such as intimal hyperplasia (IH) or atherosclerosis.

METHODS

We performed transient computational fluid dynamics simulations within idealized three-dimensional models of 'end-to-side' and 'end-to-end' radio-cephalic anastomosis, using non-Newtonian blood and previously measured flows and division ratio in subjects requiring primary access procedure as boundary conditions.

RESULTS

The numerical simulations allowed full characterization of blood flow inside the AVF and of patterns of haemodynamic shear stress, known to be the major determinant of vascular remodelling and disease. Wall shear stress was low and oscillating in zones where flow stagnation occurs on the artery floor and on the inner wall of the juxta-anastomotic vein.

CONCLUSIONS

Zones of low and oscillatory shear stress were located in the same sites where luminal reduction was documented in previous experimental studies on sites stenosis distribution in AVF. We conclude that even when exposed to high flow rates, there are spot regions along the AVF exposed to athero-prone shear stress that favour vessel stenosis by triggering IH.

Coronary Artery Bypass Grafting With Y-Saphenous Vein Grafts

Introduction: The saphenous vein is one of the indispensible grafts for coronary revascularization despite the advantages of arterial grafts over veins. It can be used in different configurations with different anastomosis (eg, sequential, composite, or Y-graft) techniques. Our aim was to investigate early and midterm results of Y-type anastomosis of saphenous vein grafts for complete coronary revascularization. Material and methods: Coronary artery bypass grafting (CABG) with Y-graft technique was performed in 512 patients between February 1998 and June 2007. In total, 608 saphenous Y coronary anastomoses were performed. These anastomoses were on first and second obtuse marginal arteries (n: 323), first diagonal and first obtuse marginal arteries (n: 187), posterolateral and posterior descending artery (n: 79), and right coronary artery and posterior descending artery (n: 19). Endareterectomy was performed in 28 patients with severely calcified coronary arteries. Patients were evaluated for early and late survival, newly developing cardiac events, recurring angina, and reinterventions. Results: In the early postoperative period, new myocardial infarction (MI) occurred in 27 (5.2%) patients and mortality in 13 (2.5%). Follow-up included the results of 487 (98%) patients. Mean follow-up duration was 56 ± 24 months. Late mortality occurred in 36 (7.3%) patients, and in 13 (2.6%) patients new MI developed in the remote follow-up. Overall survival including all deaths at 3, 5, and 7 years was 94 ± 0.6%, 86 ± 1.3%, and 83 ± 2.1%, respectively, and actuarial freedom from angina recurrence at 3, 5, and 7 years was 95.2 ± 2.5%, 86.4 ± 3%, and 84.7 ± 4.6%, respectively. Among long-term survivors, 116 patients (25.7%), 49 being symptomatic, with 123 saphenous Y-type anastomoses having undergone angiography studies. Saphenous vein Y grafts were completely patent in 94 anastomoses (76.4%). Conclusions: Saphenous vein Y-type anastomosis technique can safely be used in patients with multivessel coronary artery disease (CAD) with successful long-term outcomes. As with sequential anastomosis, the safety of the technique may be attributed to the distribution of inflow from aorta into multiple vessels.

A method to estimate wall shear rate with a clinical ultrasound scanner

A simple technique to estimate the wall shear rate in healthy arteries using a clinical ultrasound scanner has been developed. This method uses the theory of fully developed oscillatory flow together with a spectral Doppler trace and an estimate of mean arterial diameter. A method using color flow imaging was compared with the spectral Doppler method in vascular phantoms and found to have errors that were on average 35% greater. Differences from the theoretic value for the time averaged wall shear rate using the spectral Doppler method varied by artery: brachial -9 (1) %; carotid -7 (1) %; femoral -22 (4) %; and fetal aorta -17 (10) %. Test measurements obtained from one healthy volunteer demonstrated the feasibility of the technique in vivo.

Validation of numerical simulation with PIV measurements for two anastomosis models

Hemodynamics is widely believed to influence coronary artery bypass graft (CABG) stenosis. Although distal anastomosis has been extensively investigated, further studies on proximal anastomosis are still necessary, as the extent and initiation of the stenosis process may be influenced by the flow of the proximal anastomosis per se. Therefore, in this study, two models (i.e. 90 degrees and 135 degrees anastomotic models) were designed and constructed to simulate a proximal anastomosis of CABG for the left and right coronary arteries, respectively. Flow characteristics for these models were studied experimentally in order to validate the simulation results found earlier. PIV measurements were carried out on two Pyrex glass models, so that the disturbed flow (stagnation point, flow separation and vortex) found in both proximal anastomosis models using numerical simulation, could be verified. Consequently, a fair agreement between numerical and experimental data was observed in terms of flow characteristics, velocity profiles and wall shear stress (WSS) distributions under both steady and pulsatile flow conditions. The discrepancy was postulated to be due to the difference in detailed geometry of the physical and computational models, due to manufacturing limitations. It was not possible to reproduce the exact shape of the computational model when making the Pyrex glass model. The analysis of the hemodynamic parameters based on the numerical simulation study also suggested that the 135 degrees proximal anastomosis model would alleviate the potential of intimal thickening and/or atherosclerosis, more than that of a 90 degrees proximal anastomosis model, as it had a lower variation range of time-averaged WSS and the lower segmental average of WSSG.

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.

Microvascular stress analysis

PURPOSE OF THE STUDY

To develop a finite element model (FEM) to study the effect of the stress and strain, in microvascular anastomoses that result from the geometrical mismatch of anastomosed vessels.

MATERIAL AND METHODS

FEMs of end-to-end and end-to-side anastomoses were constructed. Simulations were made using finite element software (NISA). We investigated the angle of inset in the end-to-side anastomosis and the discrepancy in the size of the opening in the vessel between the host and recipient vessels. The FEMs were used to predict principal and shear stress and strain at the position of each node.

RESULTS

Two types of vascular deformation were predicted during different simulations: longitudinal distortion, and rotational distortion. Stress values ranged from 151.1 to 282.4MPa for the maximum principal stress, from -122.9 to -432.2MPa for the minimum principal stress, and from 122.1 to 333.1MPa for the maximum shear stress. The highest values were recorded when there was a 50% mismatch in the diameter of the vessels at the site of the end-to-end anastomosis.

CONCLUSION

The effect of the vessel's size discrepancy on the blood flow and deformation was remarkable in the end-to-end anastomosis. End-to-side anastomosis was superior to end-to-end anastomosis. FEM is a powerful tool to study vascular deformation, as it predicts deformation and biomechanical processes at sites where physical measurements are likely to remain impossible in living humans.

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.

Investigations into the relationship between hemodynamics and vascular alterations in an established arteriovenous fistula

Arteriovenous fistula are specific vessels created by a vascular operation in order to provide sufficient blood access for extracorporeal circulation in hemodialysis. They are subject to numerous pathologies that may be caused by hemodynamic effects. To better understand these effects, a specific patient's arteriovenous fistula was reconstructed from computed tomography angiography. Computational fluid dynamics software made it possible to solve fluid mechanics equations under physiological conditions. An accurate map of unsteady velocity profiles and wall shear stress was drawn up. The computed velocity profiles were successfully confronted with Echo Doppler investigation. Selected regions with or without calcification, the end stage of wall alteration, were examined in terms of the mechanical constraints generated by blood flow. In contrast with other authors, we did not observe any association between calcification and areas of oscillating shear stress. Nevertheless, a statistical analysis of the whole vessel envelop and specific sites of calcification suggested a potential association between calcification and high temporal wall shear stress gradients.

Numerical Simulation of Wall Shear Stress and Particle-Based Hemodynamic Parameters in Pre-Cuffed and Streamlined End-to-Side Anastomoses

A number of research studies have related multiple hemodynamic parameters to the formation of distal anastomotic intimal hyperplasia (IH) at the sub-cellular, cellular, and tissue levels. Focusing on mitigating WSS-based parameters alone, several studies have suggested geometrically modified end-to-side anastomoses with the intent of improving synthetic graft patency rates. However, recent clinical trials of commercially available versions of these grafts indicate persistently high rates of failure. Furthermore, recent evidence suggests that platelet-wall interactions may play a significant role in the formation of IH, which is not captured by WSS-based parameters alone. In this study, numerical simulations have been conducted to assess the potential for IH formation in conventional and geometrically modified anastomoses based on both wall shear stress (WSS) conditions and platelet-wall interactions. Sites of significant particle-wall interactions, including elevated concentrations and stasis, were identified by a near-wall residence time model, which includes factors for platelet activation and surface reactivity. Conventional, pre-cuffed, and streamlined distal end-to-side anastomoses were considered with proximal and distal arterial outflow. It was found that a pre-cuffed anastomosis, similar to the Distaflo configuration, does not offer a hemodynamic advantage over the conventional design considered with respect to the magnitude of the WSS field and the potential for platelet interactions with the vessel surface. Streamlined configurations largely consistent with venous confluences resulted in an advantageous reduction of wall shear stress gradient values; however, particle-wall interactions remained significant throughout the anastomosis. Results of this study are not intended to be directly extrapolated to surgical recommendations. However, these results highlight the difficulty associated with designing an end-to-side distal anastomosis with two-way outflow that is capable of simultaneously reducing multiple hemodynamic parameters. Further testing will be necessary to determine if the observed elevated particle-wall interactions in a pre-cuffed anastomosis provide the stimulus responsible for the reported high failure rates of these grafts.

On reducing abnormal hemodynamics in the femoral end-to-side anastomosis: the influence of mechanical factors

This study was concerned with investigating the influence of mechanical factors on the hemodynamics of the end-to-side anastomosis in an attempt to identify critical factors and establish if it is possible to re-engineer existing, patient-specific, by-pass grafts with a view to increasing their patency. The study chose the femoral artery as the principal subject of interest. Wall shear stresses (WSS) and wall shear stress gradients (WSSG) were taken as the primary quantities of interest. Angle, graft calibre, interposition cuffs, proximal outflow and inlet waveform were studied. The study found that the use of cuffs and patches can significantly reduce abnormal WSS and WSSG by up to 70% when compared to a benchmark 45 degrees conventional anastomosis. The Taylor patch was found to be more robust in reducing peak WSS magnitudes and gradients than the Miller cuff, where design variables proved to be more critical. On the addition of a Taylor patch to a realistic end-to-side femoral anastomosis, the peak WSS and WSSG were found to be reduced by 27% and 57%, respectively. In conclusion, it is possible to use idealised models to identify critical disease influencing factors and to use these findings to reduce the effects of abnormal hemodynamics in realistic, patient-dependant models.

Computational simulation of biomechanics in e-PTFE and venous Miller's cuffs: implications for intimal hyperplasia

A computational distal end-to-side Miller's cuff anastomotic model was used to analyse the possible difference in intimal hyperplasia (IH) formed between e-PTFE and venous cuffs. A large strain FEA model was used to compute the strain after physiological loading and the deformed geometries used as wall boundaries for CFD analysis. Regression analysis was performed to investigate relationships between mechanical factors and prior IH. The results showed that the venous Miller's cuff anastomosis deformed twice as much as the e-PTFE cuff and that the expansion of both cuffs generated elevated strains in the artery floor while the fluid shear indices were qualitatively similar in each case. In the e-PTFE cuff, the strain and OSI correlated with IH in a proportional and equivalent manner; however, these regressions grossly over-estimated the predicted IH in the vein cuff. Thus, biomechanical effects may be important in synthetically cuffed anastomoses, but do not account for the reduced IH in venous cuffed anastomoses.

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.

Particle hemodynamics analysis of Miller cuff arterial anastomosis

OBJECTIVE

Studies of animal and human below-knee anastomoses with Miller cuffs indicate that improved graft patency results from redistribution of intimal hyperplasia away from areas critical to flow delivery, such as the arterial toe. We hypothesize that particle hemodynamic conditions are a biophysical mechanism potentially responsible for the clinically observed shift in intimal hyperplasia localization associated with better patency of the Miller configuration.

METHODS

Computational fluid dynamics analysis of vortical flow patterns, wall shear stress fields, and potential for platelet interaction with the vascular surface was performed for realistic three-dimensional conventional and Miller cuff distal end-to-side anastomoses. Sites of significant platelet-wall interaction, including elevated near-wall particle concentrations and stasis, were identified with a validated near-wall residence time model, which includes shear stress-based factors for particle activation and surface reactivity.

RESULTS

Particle hemodynamics largely coincide with the observed redistribution of intimal hyperplasia away from the critical arterial toe region. Detrimental changes in wall shear stress vector magnitude and direction are significantly reduced along the arterial suture line of the Miller cuff, largely as a result of increased anastomotic area available for flow redirection. However, because of strong particle-wall interaction, resulting high near-wall residence time contours indicate significant intimal hyperplasia along the graft-vein suture line and in the vicinity of the arterial heel.

CONCLUSIONS

While a number of interacting mechanical, biophysical, and technical factors may be responsible for improved Miller cuff patency, our results imply that particle hemodynamics conditions engendered by Miller cuff geometry provide a mechanism that may account for redistribution of intimal hyperplasia. In particular, it appears that a focal region of significant particle-wall interaction at the arterial toe is substantially reduced with the Miller cuff configuration.

Particle-hemodynamics modeling of the distal end-to-side femoral bypass: effects of graft caliber and graft-end cut

Late-stage occlusions of peripheral synthetic bypass grafts are frequently due to intimal hyperplasia and/or thrombosis at the distal anastomosis, resulting in unacceptably high failure rates. It has been widely established that hemodynamic and blood particle interactions with the vascular surface as well as surgical injury and compliance mismatch are inciting mechanisms capable of eliciting various cellular level responses associated with distal anastomotic intimal hyperplasia (IH) formation. Primary geometric factors influencing anastomotic hemodynamics include the graft-to-artery diameter ratio and graft-hood shape, which are determined by the graft caliber and initial graft-end cut selected by the vascular surgeon. In this study, the particle-hemodynamic effects of graft-end cuts (straight, curved, and S-shaped) and graft-to-artery diameter ratios (2:1 vs. 1.5:1) have been numerically assessed in four common unexpanded anastomotic configurations with respect to vortical flow patterns, wall shear stress based parameters, and platelet interactions with the vascular surface. Sites of significant platelet-wall interactions have been identified by a novel near-wall residence time (NWRT) model, which includes shear stress based factors for platelet activation and endothelial cell expression of anti-thrombogenic compounds. Of the configurations evaluated, straight and curved graft-end cuts with a graft-to-artery diameter ratio of 1.5:1 were found to reduce the particle-hemodynamic potential for IH development at locations critical to flow delivery. Nevertheless, the potential for significant IH occurrence via platelet and/or endothelial response pathways was highly evident in all conventional anastomoses considered, such that a decisively superior configuration was not determined. These results illustrate the need for alternative anastomotic designs with the intent of reducing critical hemodynamic wall parameters and mitigating regions of significant particle-wall interactions.

Internet-based system for simulation-based medical planning for cardiovascular disease

Current practice in vascular surgery utilizes only diagnostic and empirical data to plan treatments, which does not enable quantitative a priori prediction of the outcomes of interventions. We have previously described simulation-based medical planning methods to model blood flow in arteries and plan medical treatments based on physiologic models. An important consideration for the design of these patient-specific modeling systems is the accessibility to physicians with modest computational resources. We describe a simulation-based medical planning environment developed for the World Wide Web (WWW) using the Virtual Reality Modeling Language (VRML) and the Java programming language.

Computational modeling of arterial biomechanics: insights into pathogenesis and treatment of vascular disease

We review how advances in computational techniques are improving our understanding of the biomechanical behavior of the healthy and diseased cardiovascular system. Numerical modeling of biomechanics is being used in a wide variety of ways, including assessment of effects of mural and hemodynamically induced stresses on atherogenesis, development of risk measures for aneurysm rupture, improvement in interpretation of medical images, and quantification of oxygen transport in diseased and healthy arteries. Although not amenable to routine clinical use, numerical modeling of cardiovascular biomechanics is a powerful research tool.

Peak velocity determination using fast Fourier velocity encoding with minimal spatial encoding

For quantitative peak velocity determination, a technique was developed that uses Fourier velocity encoding (FVE) for the fast acquisition of images of velocity with no spatial encoding other than slice selection. The technique produces images of velocity versus temporal frequency. In applications where the quantity of interest is the peak velocity and in-plane spatial localization is not required, high SNR images are produced with reduced sensitivity to errors due to slice thickness and motion. The technique was validated using steady and pulsatile flow in a straight tube, and compared to both phase contrast measurements and numerical models using steady flow in a 50% and a 75% cosinusoidal stenosis phantom. Results show that for slices as large as 2 cm and/or undergoing periodic motion, FVE can accurately measure the peak velocity in cases where a distribution of velocities exist.

Numerical investigation of the haemodynamics at a patched arterial bypass anastomosis

Intimal hyperplasia at arterial bypass graft anastomoses is a major factor responsible for graft failure. A revised surgical technique, incorporating a Taylor vein patch into the distal anastomosis of PTFE grafts, results in a decrease in intimal hyperplasia and improved patency rates. Numerical simulations of pulsatile, non-Newtonian blood flow through life-like femorodistal bypass models have been performed to determine whether haemodynamic benefits arise from the modified geometry of the Taylor anastomosis. In a conventional bypass, the distal anastomotic flow exhibited considerable spatial and temporal variations. Steep spatial gradients in the shearing force acted along the floor during systole. The effect of the Taylor geometry was to reduce gradually the momentum of the blood approaching the junction. Thus, flow disturbances were abated, undesirable flow separation at the toe was diminished, and a less adverse floor shear stress distribution prevailed in that case. Intimal thickening should be alleviated at the toe in the Taylor model where separation is reduced, and where the thrombogenic graft surface is replaced with a vein patch. Intimal hyperplasia on the floor may be inhibited in the Taylor model due to more favourable shear stresses. The improved flow through the patched anastomosis should contribute to its enhanced performance.

Coupled computational analysis of arterial LDL transport -- effects of hypertension

Hypertension, a risk factor for atherosclerosis, increases the uptake of low density lipoproteins (LDL) by the arterial wall. Our objective in this work was to use computational modeling to identify physical factors that could be partially responsible for this effect. Fluid flow and mass transfer patterns in the lumen and wall of an arterial model were computed in a coupled manner, replicating as closely as possible previous experimental studies in which LDL uptake into the artery wall was measured in straight, excised arterial segments. Under conditions of both flow and no-flow, simulations predicted an increase in concentration polarization of LDL at the artery wall when arterial pressure was increased from 120 to 160 mmHg. However, this led to only a slight increase in mean LDL concentration within the arterial wall. However, if the permeability of the endothelium to LDL was allowed to vary with intra-arterial pressure, then the simulations predicted that the uptake of LDL would be enhanced 1.9-2.6 fold at higher pressure. The magnitude of this increase was consistent with experimental data. We conclude that the concentration polarization effects, enhanced by elevated intra-arterial pressure, cannot explain the increase in LDL uptake seen under hypertensive conditions. Instead, the data are most consistent with a pressure-linked increase in endothelial permeability to LDL.

Flow instabilities in a graft anastomosis: a study of the instantaneous velocity fields

The major cause of arterial bypass graft failure is intimal hyperplasia. Fluctuating wall shear stresses in the graft, which are associated with disturbed flow, are believed to be important factors in the development and localization of intimal hyperplasia. This study, based upon water as the working fluid, has investigated the flow structure inside a 30 degree Y-junction with different fillet radii at the intersection between the graft and the host artery at various Reynolds numbers and distal outlet segment (DOS) to proximal outlet segment (POS) flow ratios. The structure of the flow has been investigated experimentally using particle image velocimetry (PIV). The two-dimensional instantaneous velocity fields confirm the existence of a very complex flow, especially in the toe and heel regions for the different fillet radii and clearly identify features such as sinks, sources, vortices and strong time dependency.

Computational analysis of coupled blood-wall arterial LDL transport

The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.

Numerical study of hemodynamics and wall mechanics in distal end-to-side anastomoses of bypass grafts

The development and progress of distal anastomotic intimal hyperplasia seems to be promoted by altered flow conditions and intramural stress distributions at the region of the artery-graft junction of vascular bypass configurations. From clinical observations, it is known that intimal hyperplasia preferentially occurs at outflow anastomoses of prosthetic bypass grafts. In order to gain a deeper insight into post-operative disease processes, and subsequently, to contribute to the development of improved vascular reconstructions with respect to long term patency rates, detailed studies are required. In context with in vivo experiments, this study was designed to analyze the flow dynamics and wall mechanics in anatomically correct bypass configurations related to two different surgical techniques and resulting geometries (conventional geometry and Miller-cuff). The influence of geometric conditions and of different compliance of synthetic graft, the host artery and the interposed venous cuff on the hemodynamic behavior and on the wall stresses are investigated. The flow studies apply the time-dependent, three-dimensional Navier-Stokes equations describing the motion of an incompressible Newtonian fluid. The vessel walls are described by a geometrically non-linear shell structure. In an iterative coupling procedure, the two problems are solved by means of the finite element method. The numerical results demonstrate non-physiological flow patterns in the anastomotic region. Strongly skewed axial velocity profiles and high secondary velocities occur downstream the artery-graft junction. On the artery floor opposite the junction, flow separation and zones of recirculation are found. The wall mechanical studies show that increased compliance mismatch leads to increased intramural stresses, and thus, may have a proliferative influence on suture line hyperplasia, as it is observed in the in vivo study.

Intimal hyperplasia and wall shear in arterial bypass graft distal anastomoses: an in vivo model study

The observation of intimal hyperplasia at bypass graft anastomoses has suggested a potential interaction between local hemodynamics and vascular wall response. Wall shear has been particularly implicated because of its known effects upon the endothelium of normal vessels and, thus, was examined as to its possible role in the development of intimal hyperplasia in arterial bypass graft distal anastomoses. Tapered (4-7 mm I.D.) e-PTFE synthetic grafts 6 cm long were placed as bilateral carotid artery bypasses in six adult, mongrel dogs weighing between 25 and 30 kg with distal anastomotic graft-to-artery diameter ratios (DR) of either 1.0 or 1.5. Immediately following implantation, simultaneous axial velocity measurements were made in the toe and artery floor regions in the plane of the anastomosis at radial increments of 0.35 mm, 0.70 mm, and 1.05 mm using a specially designed 20 MHz triple crystal ultrasonic wall shear rate transducer Mean, peak, and pulse amplitude wall shear rates (WSRs), their absolute values, the spatial and temporal wall shear stress gradients (WSSG), and the oscillatory shear index (OSI) were computed from these velocity measurements. All grafts were harvested after 12 weeks implantation and measurements of the degree of intimal hyperplasia (IH) were made along the toe region and the artery floor of the host artery in 1 mm increments. While some IH occurred along the toe region (8.35+/-23.1 microm) and was significantly different between DR groups (p<0.003), the greatest amount occurred along the artery floor (81.6+/-106.5 microm, mean +/- S.D.) (p < 0.001) although no significant differences were found between DR groups. Linear regressions were performed on the paired IH and mean, peak, and pulse amplitude WSR data as well as the absolute mean, peak, and pulse amplitude WSR data from all grafts. The mean and absolute mean WSRs showed a modest correlation with IH (r = -0.406 and -0.370, respectively) with further improvements seen (r = -0.482 and -0.445, respectively) when using an exponential relationship. The overall best correlation was seen against an exponential function of the OSI (r = 0.600). Although these correlation coefficients were not high, they were found to be statistically significant as evidenced by the large F-statistic obtained. Finally, it was observed that over 75 percent of the IH occurred at or below a mean WSR value of 100 s(-1) while approximately 92 percent of the IH occurred at or below a mean WSR equal to one-half that of the native artery. Therefore, while not being the only factor involved, wall shear (and in particular, oscillators wall shear) appears to provide a stimulus for the development of anastomotic intimal hyperplasia.

Effects of anastomotic angle on vascular tissue responses at end-to-side arterial grafts

OBJECTIVE

Hemodynamics has been implicated in the late failure of arterial bypass grafts, which frequently occurs at the distal anastomosis site. This study was designed to assess the relationship between local hemodynamics and pathologic responses of the distal anastomosis by manipulation of the angle of anastomosis of the graft, a major determinant of local hemodynamics.

METHODS

End-to-side anastomoses of the right carotid to the left carotid arteries of rabbits were performed at anastomotic angles of less than 10 degrees (acute), 45 degrees (intermediate), or 90 degrees (right angle), and then the upstream left carotid arteries were ligated to simulate pathologic occlusion. We examined tissue responses on the wall of the recipient vessel opposite the anastomosis site (the bed), where unusual hemodynamic forces are imposed.

RESULTS

Three months after surgery, intimal thickening was observed on the upstream portion of the acute, and more rarely, the intermediate anastomoses only. Medial thinning caused by loss of cells and matrix, and an aneurysm-like dilation, was observed in the right angle and some intermediate anastomoses, but not in the acute anastomoses. En face confocal microscopy at 3 weeks after surgery revealed severe disruption of the internal elastic lamina in all anastomotic models. Zymography and Western immunoblotting demonstrated gelatinolytic activity, caused by expression and activation of MMP-2, that was lowest in the acute anastomoses, higher in the intermediate anastomoses, and highest in the right-angle anastomoses.

CONCLUSIONS

We infer that very different pathologic changes to the vessel wall are elicited when local hemodynamics is manipulated by altering the anastomotic branch angle.

The effect of proximal artery flow on the hemodynamics at the distal anastomosis of a vascular bypass graft: computational study

The formation of distal anastomotic intimal hyperplasia (IH), one common mode of bypass graft failure, has been shown to occur in the areas of disturbed flow particular to this site. The nature of theflow in the segment of artery proximal to the distal anastomosis varies from case to case depending on the clinical situation presented. A partial stenosis of a bypassed arterial segment may allow residual prograde flow through the proximal artery entering the distal anastomosis of the graft. A complete stenosis may allow for zero flow in the proximal artery segment or retrograde flow due to the presence of small collateral vessels upstream. Although a number of investigations on the hemodynamics at the distal anastomosis of an end-to-side bypass graft have been conducted, there has not been a uniform treatment of the proximal artery flow condition. As a result, direct comparison of results from study to study may not be appropriate. The purpose of this work was to perform a three-dimensional computational investigation to study the effect of the proximal artery flow condition (i.e., prograde, zero, and retrograde flow) on the hemodynamics at the distal end-to-side anastomosis. We used the finite volume method to solve the full Navier-Stokes equations for steady flow through an idealized geometry of the distal anastomosis. We calculated the flow field and local wall shear stress (WSS) and WSS gradient (WSSG) everywhere in the domain. We also calculated the severity parameter (SP), a quantification of hemodynamic variation, at the anastomosis. Our model showed a marked difference in both the magnitude and spatial distribution of WSS and WSSG. For example, the maximum WSS magnitude on the floor of the artery proximal to the anastomosis for the prograde and zero flow cases is 1.8 and 3.9 dynes/cm2, respectively, while it is increased to 10.3 dynes/cm2 in the retrograde flow case. Similarly, the maximum value of WSSG magnitude on thefloor of the artery proximal to the anastomosis for the prograde flow case is 4.9 dynes/cm3, while it is increased to 13.6 and 24.2 dynes/cm3, respectively, in the zero and retrograde flow cases. The value of SP is highest for the retrograde flow case (13.7 dynes/cm3) and 8.1 and 12.1 percent lower than this for the prograde (12.6 dynes/cm3) and zero (12.0 dynes/cm3) flow cases, respectively. Our model results suggest that the flow condition in the proximal artery is an important determinant of the hemodynamics at the distal anastomosis of end-to-side vascular bypass grafts. Because hemodynamic forces affect the response of vascular endothelial cells, the flow situation in the proximal artery may affect IH formation and, therefore, long-term graft patency. Since surgeons have some control over the flow condition in the proximal artery, results from this study could help determine which flow condition is clinically optimal.

Pulsatile flow in an end-to-side vascular graft model: comparison of computations with experimental data

Various hemodynamic factors have been implicated in vascular graft intimal hyperplasia, the major mechanism contributing to chronic failure of small-diameter grafts. However, a thorough knowledge of the graft flow field is needed in order to determine the role of hemodynamics and how these factors affect the underlying biological processes. Computational fluid dynamics offers much more versatility and resolution than in vitro or in vivo methods, yet computations must be validated by careful comparison with experimental data. Whereas numerous numerical and in vitro simulations of arterial geometries have been reported, direct point-by-point comparisons of the two techniques are rare in the literature. We have conducted finite element computational analyses for a model of an end-to-side vascular graft and compared the results with experimental data obtained using laser-Doppler velocimetry. Agreement for velocity profiles is found to be good, with some clear differences near the recirculation zones during the deceleration and reverse-flow segments of the flow waveform. Wall shear stresses are determined from velocity gradients, whether by computational or experimental methods, and hence the agreement for this quantity, while still good, is less consistent than for velocity itself from the wall shear stress numerical results, we computed four variables that have been cited in the development of intiimal hyperplasia-the time-averaged wall shear stress, an oscillating shear index, and spatial and temporal wall shear stress gradients in order to illustrate the versatility of numerical methods. We conclude that the computational approach is a valid alternative to the experimental approach for quantitative hemodynamic studies. Where differences in velocity were found by the two methods, it was generally attributed to the inability of the numerical method to model the fluid dynamics when flow conditions are destabilizing. Differences in wall shear, in the absence of destabilizing phenomena, were more likely to be caused by difficulties in calculating wall shear from relatively low resolution in vitro data.

Comparison of Two Different Arteriovenous Anastomotic Forms By Numerical 3D Simulation of Blood Flow

Anastomotic intimal hyperplasia caused by unphysiological hemodynamics is generally accepted as a reason for dialysis access graft occlusion. Optimizing the venous anastomosis can improve the patency rate of arteriovenous grafts. The purpose of this study was to examine, evaluate and characterize the local hemodynamics, and in particular, wall shear stresses in conventional venous end-to-side anastomosis and in patch form anastomosis (Venaflotrade mark) by Computational Fluid Dynamics (CFD). The flow simulations were carried out as three-dimensional to extend results of our previous 2D studies. The numerical simulation was done with a finite volume-based algorithm. The anastomotic forms were constructed with usual size and fixed walls. Subdividing the flow domain into multiple control volumes solved the fundamental equations. The boundary conditions were constant for both forms. The velocity profile of the patch form is better than for the conventional form. The region of high static pressure caused on flow stagnation is reduced on the vein floor. The anastomotic wall shear stress is decreased. The results of this study strongly support patch form use to reduce the incidence of intimal hyperplasia and venous anastomotic stenoses.

Blood flow in distal end-to-side anastomoses with PTFE and a venous patch: results of an in vitro flow visualisation study

OBJECTIVES

non-physiological flow behaviour plays a significant role in the development of distal anastomotic intimal hyperplasia. To investigate flow patterns in four anastomotic types of femoral end-to-side distal bypass graft anastomoses, a flow visualisation study was performed.

METHODS

transparent 1:1 casted replicas of distal vascular graft anastomoses created by conventional technique, Miller-cuff, Taylor- and Linton-patch were fabricated. A pulsatile mock circulation with a high-speed video system was constructed. Flow pattern was determined at mean Reynolds numbers 100-500. Migrations of the stagnation points on the bottom of the anastomoses at mean Reynolds numbers 100, 230, and 350 were measured.

RESULTS

a vortex forms during early systole and increases to maximum systole in all anastomoses. During the diastolic phase the vortex moves in the Miller-cuff distally to the toe of the anastomosis and remains standing, while in the other anastomotic types the vortex moves proximally to the heal of the junction and breaks down. The shift of the stagnation point in the Miller-cuff was considerably smaller than in the other anastomoses.

CONCLUSION

conventional, Linton and Taylor anastomoses show similar flow patterns. The Miller-cuff with its wider cavity shows lower shift of the bottom stagnation point, but a persistent washout of the anastomotic cavity, which may contribute to its reported good clinical performance.

A numerical study of blood flow patterns in anatomically realistic and simplified end-to-side anastomoses

PURPOSE

Recently, some numerical and experimental studies of blood flow in large arteries have attempted to accurately replicate in vivo arterial geometries, while others have utilized simplified models. The objective of this study was to determine how much an anatomically realistic geometry can be simplified without the loss of significant hemodynamic information.

METHOD

A human femoral-popliteal bypass graft was used to reconstruct an anatomically faithful finite element model of an end-to-side anastomosis. Nonideal geometric features of the model were removed in sequential steps to produce a series of successively simplified models. Blood flow patterns were numerically computed for each geometry, and the flow and wall shear stress fields were analyzed to determine the significance of each level of geometric simplification.

RESULTS

The removal of small local surface features and out-of-plane curvature did not significantly change the flow and wall shear stress distributions in the end-to-side anastomosis. Local changes in arterial caliber played a more significant role, depending upon the location and extent of the change. The graft-to-host artery diameter ratio was found to be a strong determinant of wall shear stress patterns in regions that are typically associated with disease processes.

CONCLUSIONS

For the specific case of an end-to-side anastomosis, simplified models provide sufficient information for comparing hemodynamics with qualitative or averaged disease locations, provided the "primary" geometric features are well replicated. The ratio of the graft-to-host artery diameter was shown to be the most important geometric feature. "Secondary" geometric features such as local arterial caliber changes, out-of-plane curvature, and small-scale surface topology are less important determinants of the wall shear stress patterns. However, if patient-specific disease information is available for the same arterial geometry, accurate replication of both primary and secondary geometric features is likely required.

The effect of graft caliber upon wall shear within in vivo distal vascular anastomoses

Wall shear has been widely implicated as a contributing factor in the development of intimal hyperplasia in the anastomoses of chronic arterial bypass grafts. Earlier studies have been restricted to either: (1) in vitro or computer simulation models detailing the complex hemodynamics within an anastomosis without corresponding biological responses, or (2) in vivo models that document biological effects with only approximate wall shear information. Recently, a specially designed pulse ultrasonic Doppler wall shear rate (PUDWSR) measuring device has made it possible to obtain three near-wall velocity measurements nonintrusively within 1.05 mm of the vessel luminal surface from which wall shear rates (WSRs) were derived. It was the purpose of this study to evaluate the effect of graft caliber, a surgically controllable variable, upon local hemodynamics, which, in turn, play an important role in the eventual development of anastomotic hyperplasia. Tapered (4-7 mm I.D.) 6-cm-long grafts were implanted bilaterally in an end-to-side fashion with 30 deg proximal and distal anastomoses to bypass occluded common carotid arteries of 16 canines. The bypass grafts were randomly paired in contralateral vessels and placed such that the graft-to-artery diameter ratio, DR, at the distal anastomosis was either 1.0 or 1.5. For all grafts, the average Re was 432 +/- 112 and the average Womersley parameter, alpha, was 3.59 +/- 0.39 based on artery diameter. There was a sharp skewing of flow toward the artery floor with the development of a stagnation point whose position varied with time (up to two artery diameters) and DR (generally more downstream for DR = 1.0). Mean WSRs along the artery floor for DR = 1.0 and 1.5 were found to range sharply from moderate to high retrograde values (589 s-1 and 1558 s-1, respectively) upstream to high antegrade values (2704 s-1 and 2302 s-1, respectively) immediately downstream of the stagnation point. Although there were no overall differences in mean and peak WSRs between groups, there were significant differences (p < 0.05) in oscillatory WSRs as well as in the absolute normalized mean and peak WSRs between groups. There were also significant differences (p < 0.05) in mean and peak WSRs with respect to axial position along the artery floor for both DR cases. In conclusion, WSR varies widely (1558 s-1 retrograde to 2704 s-1 antegrade) within end-to-side distal graft anastomoses, particularly along the artery floor, and may play a role in the development of intimal hyperplasia through local alteration of mass transport and mechano-signal transduction within the endothelium.

Flow waveform effects on end-to-side anastomotic flow patterns

PURPOSE

Restenosis due to distal anastomotic intimal hyperplasia, a leading cause of arterial bypass graft failure, is thought to be promoted by hemodynamic effects, specifically 'abnormal' wall shear stress patterns. The purpose of this study was to quantify the effects of flow waveform on peri-anastomotic flow and wall shear stress patterns.

METHODS

Blood flow and wall shear stress patterns were numerically computed in a representative three-dimensional anastomosis using femoral, iliac and coronary flow waveforms suitable for humans at rest. Numerical results were validated against experimental data.

RESULTS

Peri-anastomotic wall shear stress patterns were influenced by a complex interplay between secondary flow effects and unsteadiness. Peripheral flow waveforms (iliac, femoral) produced large temporal and spatial wall shear stress gradients on the host artery bed. In comparison, the coronary flow waveform produced normalized bed wall shear stress gradients that were a factor of 2-3 less than for the peripheral waveforms, even though average bed wall shear stress magnitudes were similar for the two waveforms.

CONCLUSIONS

If anastomotic intimal hyperplasia is promoted by large spatial and/or temporal gradients of wall shear stress, as has been proposed, this study predicts that there will be markedly less intimal hyperplasia on the host artery bed of coronary bypass grafts than for peripheral bypass grafts. This information, in conjunction with a comparative histopathologic study of intimal hyperplasia distribution, could help determine specific wall shear stress factors promoting intimal hyperplasia.

Compliance mismatch may promote graft-artery intimal hyperplasia by altering suture-line stresses

The role of graft-artery compliance mismatch in the development of distal anastomotic intimal hyperplasia (DAIH) is not yet resolved. Although DAIH develops at all surgically created anastomoses, increased compliance mismatch does not lead to greater hyperplasia formation in end-to-end anastomoses, but in end-to-side anastomoses, it leads to a profound increase in hyperplasia. The current study was undertaken to determine whether suture-induced anastomotic stresses could explain these findings. A large strain finite element analysis of vascular wall mechanics was performed to compare the influence of compliance mismatch on intramural stresses in end-to-end versus end-to-side anastomoses. A novel modelling approach was implemented which includes suture-induced stress concentrations. End-to-end and end-to-side graft-artery simulations were executed using (1) artery (compliance = C = 0.44% kPa(-1)), (2) vein (C = 0.33% kPa(-1)), and (3) Dacron (C = 0.14% kPa(-1)) grafts. Residual stresses due to axial tension were included and the anastomoses were statically inflated to 13.3 kPa (100 mmHg). Elevated intramural stresses were found to exist at both the end-to-end and end-to-side graft-artery junctions; however, in the end-to-end anastomosis, the maximum anastomotic stress was not a function of the graft compliance, whereas in the end-to-side anastomosis, the maximum stress was a strong function of graft compliance. For the 45 degree end-to-side geometry considered in this study, the maximum anastomotic stress concentration obtained using a stiff Dacron graft was more than 40% greater than that obtained using a compliant artery graft. In the end-to-end anastomosis, the Dacron graft led to a less than 5% increase in maximum stress over the artery graft. Therefore, increased compliance mismatch increases stresses and promotes DAIH in end-to-side junctions, but, it has little influence on either stresses or DAIH in end-to-end junctions. Thus, the proliferative influence of increased compliance mismatch on suture-line hyperplasia in end-to-side anastomoses can be explained by the resulting increase in intramural stresses. In addition, since high stresses were found in both geometries, elevated suture-line intramural stresses may be an important proliferative stimulus for intimal hyperplasia formation in all vascular reconstructions.

The assignment of velocity profiles in finite element simulations of pulsatile flow in arteries

In this paper we present a new method for the assignment of pulsatile velocity profiles as input boundary conditions in finite element models of arteries. The method is based on the implementation of the analytical solution for developed pulsatile flow in a rigid straight tube. The analytical solution provides the fluid dynamics of the region upstream from the fluid domain to be investigated by means of the finite element approach. In standard fluid dynamics finite element applications, the inlet developed velocity profiles are achieved assuming velocity boundary conditions to be easily implementable-such as flat or parabolic velocity profiles-applied to a straight tube of appropriate length. The tube is attached to the inflow section of the original fluid domain so that the flow can develop fully. The comparison between the analytical solution and the traditional numerical approach indicates that the analytical solution has some advantages over the numerical one. Moreover, the results suggest that subroutine employment allows a consistent reduction in solving time especially for complex fluid dynamic model, and significantly decreases the storage and memory requirements for computations.

In-vivo measurements of blood flow velocity profiles in canine ilio-femoral anastomotic bypass grafts

In-vivo velocity profiles were recorded with a 20 MHz 80-channel pulsed Doppler ultrasound velocimeter in canine end-to-side ilio-femoral anastomotic grafts. The geometries were obtained from casts of the anastomotic region, and flow rates were measured with electromagnetic flow probes. Three cases reported here include a "standard" geometry, which was similar to previously studied in vitro models, a stenosed geometry, and a case with below average flow rate. Observed flow features include separation at the hood and toe, movement of the floor stagnation point, and skewed profiles in the proximal outflow segment. Out-of-plane curvature and lateral displacement of the anastomosis inlet appear to have a strong effect on the flow fields. In addition, compliance affects the instantaneous flow rates within the proximal and distal branches.

Numerical study of wall mechanics and fluid dynamics in end-to-side anastomoses and correlation to intimal hyperplasia

In order to analyse the wall mechanics and the flow dynamics in compliant vascular distal end-to-side anastomoses, computer simulation has been performed. In a model study the effect of compliance mismatch on the wall displacements and on the intramural stresses as well as the influence of wall distensibility on the flow patterns are demonstrated applying two distensible models with different graft elasticity. In addition, the flow in a rigid model simulating a vein graft without adaption of the venous lumen has been investigated. The geometries for these models were obtained from a concurrent experimental study, where the formation of distal anastomotic intimal hyperplasia (DAIH) was studied in untreated and externally stiffened autologous venous grafts in sheep. In the flow study the time-dependent, three-dimensional Navier-Stokes equations describing the motion of an incompressible Newtonian fluid are applied. The vessel wall is modelled using a geometrically non-linear shell structure. In an iteratively coupled approach the transient shell equations and the governing fluid equations are solved numerically using the finite element method. In both compliant models maximum displacement and areas of steep stress gradients are observed in the junction region along the graft-artery intersection. The comparison of the normal deformations and the distribution and magnitude of intramural stress shows quantitative differences. The graft elasticity acts as a regulating factor for the deformability and the stress concentration in the junction area: In the model with high graft-elasticity maximum normal deformation at the side wall is 17%. This is twice as large as in the stiff graft model and maximum principle stress at the inner surface differs by one order of magnitude. The numerical results concerning the flow patterns indicate strongly skewed axial velocity profiles downstream of the junction, large secondary motion, flow separation and recirculation on the artery floor opposite the junction and at the inner wall downstream of the toe. In these regions a correlation between the time-averaged fluid wall shear stress and intimal thickening found in the animal experiment can be observed, whereas the pronounced formation of DAIH at the suture line seems to be mainly dependent on wall mechanical factors such as intramural stress and strain.