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).     

Comparison of the hemodynamics in 6mm and 4-7 mm hemodialysis grafts by means of CFD

The aim of our study is to investigate with computational fluid dynamics (CFD) whether different arterial anastomotic geometries result in a different hemodynamics at the arterial (AA) and venous anastomosis (VA) of hemodialysis vascular access grafts. We have studied a 6mm graft (CD) and a 4-7 mm graft (TG). A validated three-dimensional CFD model is developed to simulate flow in the two graft types. Only the arterial anastomosis (AA) geometry differs. The boundary conditions applied are a periodic velocity signal at the arterial inlet and a periodic pressure wave at the venous outlet. Flow rate is set to 1,000 ml/min. The time dependent Navier-Stokes equations are solved. Wall shear stress (WSS), wall shear stress gradient (WSSG) and pressure gradient (PG) are calculated. Anastomotic flow is asymmetric although the anastomosis geometry is symmetric. The hemodynamic parameters, WSS, WSSG and PG, values at the suture line of the arterial anastomosis of the TG are at least twice as much as in the CD. Comparing the parameters at the two AA indicate that little flow rate increase introduces the risk of hemolysis in the TG whereas the CD is completely free of hemolysis. The hemodynamic parameter values at the venous anastomosis of the CD are 24 till 35% higher compared to the values of the TG. WSS values (> 3 Pa) in the VA are in the critical range for stenosis development in both graft geometries. The zones where the parameters reach extreme values correspond to the locations where intimal hyperplasia formation is reported in literature. In all anastomoses, the hemodynamic parameter levels are in the range where leucocytes and platelets get activated. Our simulations confirm clinical results where TG did not show a better outcome when compared to the CD.     

A simple fluid–structure coupling algorithm for the study of the anastomotic mechanics of vascular grafts

Vascular anastomoses constitute a main factor in poor graft performance due to mismatches in distensibility between the host artery and the graft. This work aims at computational fluid–structure investigations of proximal and distal anastomoses of vein grafts and synthetic grafts. Finite element and finite volume models were developed and coupled with a user-defined algorithm. Emphasis was placed on the simplicity of the coupling algorithm. An artery and vein graft showed a larger dilation mismatch than an artery and synthetic graft. The vein graft distended nearly twice as much as the artery while the synthetic graft displayed only approximately half the arterial dilation. For the vein graft, luminal mismatching was aggravated by development of an anastomotic pseudo-stenosis. While this study focused on end-to-end anastomoses as a vehicle for developing the coupling algorithm, it may serve as useful point of departure for further investigations such as other anastomotic configurations, refined modelling of sutures and fully transient behaviour.     

Can sites prone to flow induced vascular complications in a-v fistulas be assessed using computational fluid dynamics?

Arterio-venous fistulas (shunts between arteries and veins) are the preferred vascular access for hemodialysis. Despite their superior patency, compared with synthetic tubes and grafts, functional problems and inadequate flow rates are the common complications. Local flow conditions, in particular low and oscillating wall shear stresses (WSS), are central to vascular problems and a robust framework for analyzing flow conditions in vascular structures could provide an understanding of the mechanisms leading to vascular complications, such as stenoses, aneurisms, and thromboses.We hypothesize that a validated computational fluid dynamics (CFD) framework can be used to identify critical fistula configurations with elevated risk of complications. Therefore, the aim of the present study was to develop a CFD framework for analyzing fluid flow in complex vascular structures, such as arterio-venous fistulas validated by comparisons of in vitro volume flows with CFD results and flow fields from ultrasound scans with CFD simulations.Volume flows measured in vitro and CFD data differed quantitatively. However, good relative correlations exist between the data using logarithmic scales. Qualitatively, visual comparisons between ultrasound and CFD images showed good agreement between the two methods. In addition, WSS levels and the oscillatory shear index (OSI) were calculated and visualized on the model surface. The method was successfully validated and the method is deemed suitable for more thorough investigations into the field of vascular complications in a-v fistulas.     

Shear stress,vascular remodeling and neointimal formation

The role of shear stress in atherosclerosis has been well documented. However, its role in restenosis was underexposed. In this paper a novel in vivo measuring technique and several of its applications related to restenosis will be described. The technique consists of a combination of 3D reconstruction of blood vessels and computational fluid dynamics (CFD). The 3D imaging techniques use either of 3D intravascular ultrasound (IVUS) as a stand-alone technique or a fusion of biplane angiography and IVUS (ANGUS). CFD is applied in order to relate local shear stress distribution to the morphology of the vessel wall. In the applications of these techniques it will be demonstrated that shear stress plays a role in the prediction of neointimal formation in in-stent restenosis and in vascular remodeling after balloon angioplasty. Attempts to locally increase shear stress by a newly developed flow divider indicate that shear stress reduce in-stent neointimal formation by 50%.     

Recent Advances in Computational Simulation of Macro-, Meso-, and Micro-Scale Biomimetics Related Fluid Flow Problems

Over the last decade, computational methods have been intensively applied to a variety of scientific researches and engineering designs. Although the computational fluid dynamics （CFD） method has played a dominant role in studying and simulating transport phenomena involving fluid flow and heat and mass transfers, in recent years, other numerical methods for the simulations at meso- and micro-scales have also been actively applied to solve the physics of complex flow and fluid-interface interactions. This paper presents a review of recent advances in multi-scale computational simulation of biomimetics related fluid flow problems. The state-of-the-art numerical techniques, such as lattice Boltzmann method （LBM）, molecular dynamics （MD）, and conventional CFD, applied to different problems such as fish flow, electro-osmosis effect of earthworm motion, and self-cleaning hydrophobic surface, and the numerical approaches are introduced. The new challenging of modelling biomimetics problems in developing the physical conditions of self-clean hydrophobic surfaces is discussed.     

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 4D Phase-Contrast MRI Flow Measurements to Computational Fluid Dynamics Simulations of Cerebrospinal Fluid Motion in the Cervical Spine

Cerebrospinal fluid (CSF) dynamics in the cervical spinal subarachnoid space (SSS) have been thought to be important to help diagnose and assess craniospinal disorders such as Chiari I malformation (CM). In this study we obtained time-resolved three directional velocity encoded phase-contrast MRI (4D PC MRI) in three healthy volunteers and four CM patients and compared the 4D PC MRI measurements to subject-specific 3D computational fluid dynamics (CFD) simulations. The CFD simulations considered the geometry to be rigid-walled and did not include small anatomical structures such as nerve roots, denticulate ligaments and arachnoid trabeculae. Results were compared at nine axial planes along the cervical SSS in terms of peak CSF velocities in both the cranial and caudal direction and visual interpretation of thru-plane velocity profiles. 4D PC MRI peak CSF velocities were consistently greater than the CFD peak velocities and these differences were more pronounced in CM patients than in healthy subjects. In the upper cervical SSS of CM patients the 4D PC MRI quantified stronger fluid jets than the CFD. Visual interpretation of the 4D PC MRI thru-plane velocity profiles showed greater pulsatile movement of CSF in the anterior SSS in comparison to the posterior and reduction in local CSF velocities near nerve roots. CFD velocity profiles were relatively uniform around the spinal cord for all subjects. This study represents the first comparison of 4D PC MRI measurements to CFD of CSF flow in the cervical SSS. The results highlight the utility of 4D PC MRI for evaluation of complex CSF dynamics and the need for improvement of CFD methodology. Future studies are needed to investigate whether integration of fine anatomical structures and gross motion of the brain and/or spinal cord into the computational model will lead to a better agreement between the two techniques.     

Characterizaton of the Vessel Geometry,Flow Mechanics and Wall Shear Stress in the Great Arteries of Wildtype Prenatal Mouse

Introduction

Abnormal fluid mechanical environment in the pre-natal cardiovascular system is hypothesized to play a significant role in causing structural heart malformations. It is thus important to improve our understanding of the prenatal cardiovascular fluid mechanical environment at multiple developmental time-points and vascular morphologies. We present such a study on fetal great arteries on the wildtype mouse from embryonic day 14.5 (E14.5) to near-term (E18.5).

Methods

Ultrasound bio-microscopy (UBM) was used to measure blood velocity of the great arteries. Subsequently, specimens were cryo-embedded and sectioned using episcopic fluorescent image capture (EFIC) to obtain high-resolution 2D serial image stacks, which were used for 3D reconstructions and quantitative measurement of great artery and aortic arch dimensions. EFIC and UBM data were input into subject-specific computational fluid dynamics (CFD) for modeling hemodynamics.

Results

In normal mouse fetuses between E14.5–18.5, ultrasound imaging showed gradual but statistically significant increase in blood velocity in the aorta, pulmonary trunk (with the ductus arteriosus), and descending aorta. Measurement by EFIC imaging displayed a similar increase in cross sectional area of these vessels. However, CFD modeling showed great artery average wall shear stress and wall shear rate remain relatively constant with age and with vessel size, indicating that hemodynamic shear had a relative constancy over gestational period considered here.

Conclusion

Our EFIC-UBM-CFD method allowed reasonably detailed characterization of fetal mouse vascular geometry and fluid mechanics. Our results suggest that a homeostatic mechanism for restoring vascular wall shear magnitudes may exist during normal embryonic development. We speculate that this mechanism regulates the growth of the great vessels.     

A simple fluid-structure coupling algorithm for the study of the anastomotic mechanics of vascular grafts

Vascular anastomoses constitute a main factor in poor graft performance due to mismatches in distensibility between the host artery and the graft. This work aims at computational fluid-structure investigations of proximal and distal anastomoses of vein grafts and synthetic grafts. Finite element and finite volume models were developed and coupled with a user-defined algorithm. Emphasis was placed on the simplicity of the coupling algorithm. An artery and vein graft showed a larger dilation mismatch than an artery and synthetic graft. The vein graft distended nearly twice as much as the artery while the synthetic graft displayed only approximately half the arterial dilation. For the vein graft, luminal mismatching was aggravated by development of an anastomotic pseudo-stenosis. While this study focused on end-to-end anastomoses as a vehicle for developing the coupling algorithm, it may serve as useful point of departure for further investigations such as other anastomotic configurations, refined modelling of sutures and fully transient behaviour.     

Influence of the renal artery ostium flow diverter on hemodynamics and atherogenesis

The structure and function of the renal artery ostium flow diverter on the caudal side of the renal branch point were previously reported; in this study, we further evaluate the diverter?s possible functions. The protrusion of this structure into the abdominal aorta suggests that the diverter may preferentially direct blood flow to the renal arteries, and that it may also influence flow patterns and recirculation known to be involved in atherogenesis. Three-dimensional computational fluid dynamics (CFD) simulations of steady and pulsatile blood flow are performed to investigate the influence of diverter size and position, and vascular geometry, on the flow patterns and fluid mechanical forces in the neighborhood of the diverter. CFD results show that the flow diverter does affect the blood distribution; depending on the diverter?s position, the flow to the renal arteries may be increased or reduced. Calculated results also demonstrate the diverter?s effect on the wall shear stress (WSS) distribution, and suggest that the diverter contributes to an atherogenic environment in the abdominal aorta, while being atheroprotective in the renal arteries themselves. These results support previous clinical findings, and suggest directions for further clinical study. The results of this work have direct implications in understanding the physiological significance of the diverter, and its potential role in the pathophysiological development of atherosclerosis.     

Location of scaffolds in bioreactors modulates the hydrodynamic environment experienced by engineered tissues

Physical forces experienced by engineered-tissues during in vitro cultivation influence tissue growth and function. The hydrodynamic environment within bioreactors plays a decisive role in providing the necessary physical stimuli and nutrient transport to support tissue development. Our overall goal is to investigate interrelationships between the local hydrodynamic environment in the bioreactor and the structural and functional tissue properties in order to optimize the production of clinically relevant engineered-tissues. To this end, we used computational fluid dynamics (CFD) modeling to characterize the complex hydrodynamic environment in a wavy-walled bioreactor used for cultivation of tissue-engineered cartilage constructs and examined the changes in the flow field due to the presence of constructs. The flow-induced shear stress range experienced by engineered constructs cultivated in the wavy-walled bioreactor (0-0.67 dyn/cm(2)) was found to be significantly lower than that in the spinner flask (0-1.2 dyn/cm(2)), and to be modulated by the radial or axial position of the constructs. These CFD results are validated by experimental particle-image velocimetry (PIV) measurements previously reported by our group. Results from the present study indicate that the location of constructs in the bioreactor not only affected the magnitude and distribution of the shear stresses on the constructs, but also other hydrodynamic parameters, such as the directional distribution of the fluid velocity and the degree of fluid recirculation, all of which may differentially influence the development of tissue-engineered constructs.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

A communication-efficient linear system solver for large eddy simulation of jet engine noise

High-fidelity computational fluid dynamics (CFD) tools, such as the large eddy simulation technique, have become feasible in aiding the field of computational aeroacoustics (CAA) to compute noise on petascale computing platforms. CAA poses significant challenges for researchers because the computational schemes used in the CFD tools should have high accuracy, good spectral resolution, and low dispersion and diffusion errors. A high-order compact finite difference scheme, which is implicit in space, can be used for such simulations because it fulfills the requirements for CAA. Usually, this method is parallelized using a transposition scheme; however, that approach has a high communication overhead. In this paper, we discuss the use of a parallel tridiagonal linear system solver based on the truncated SPIKE algorithm for reducing the communication overhead in our large eddy simulations. We present theoretical performance analysis and report experimental results collected on two parallel computing platforms.     

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.     

Analysis of novel geometry-independent method for dialysis access pressure-flow monitoring

Background

End-stage renal disease (ESRD) confers a large health-care burden for the United States, and the morbidity associated with vascular access failure has stimulated research into detection of vascular access stenosis and low flow prior to thrombosis. We present data investigating the possibility of using differential pressure (ΔP) monitoring to estimate access flow (Q) for dialysis access monitoring, with the goal of utilizing micro-electro-mechanical systems (MEMS) pressure sensors integrated within the shaft of dialysis needles.

Methods

A model of the arteriovenous graft fluid circuit was used to study the relationship between Q and the ΔP between two dialysis needles placed 2.5–20.0 cm apart. Tubing was varied to simulate grafts with inner diameters of 4.76–7.95 mm. Data were compared with values from two steady-flow models. These results, and those from computational fluid dynamics (CFD) modeling of ΔP as a function of needle position, were used to devise and test a method of estimating Q using ΔP and variable dialysis pump speeds (variable flow) that diminishes dependence on geometric factors and fluid characteristics.

Results

In the fluid circuit model, ΔP increased with increasing volume flow rate and with increasing needle-separation distance. A nonlinear model closely predicts this ΔP-Q relationship (R² > 0.98) for all graft diameters and needle-separation distances tested. CFD modeling suggested turbulent needle effects are greatest within 1 cm of the needle tip. Utilizing linear, quadratic and combined variable flow algorithms, dialysis access flow was estimated using geometry-independent models and an experimental dialysis system with the pressure sensors separated from the dialysis needle tip by distances ranging from 1 to 5 cm. Real-time ΔP waveform data were also observed during the mock dialysis treatment, which may be useful in detecting low or reversed flow within the access.

Conclusion

With further experimentation and needle design, this geometry-independent approach may prove to be a useful access flow monitoring method.     

Local and global geometric influence on steady flow in distal anastomoses of peripheral bypass grafts

We consider the effect of geometrical configuration on the steady flow field of representative geometries from an in vivo anatomical data set of end-to-side distal anastomoses constructed as part of a peripheral bypass graft. Using a geometrical classification technique, we select the anastomoses of three representative patients according to the angle between the graft and proximal host vessels (GPA) and the planarity of the anastomotic configuration. The geometries considered include two surgically tunneled grafts with shallow GPAs which are relatively planar but have different lumen characteristics, one case exhibiting a local restriction at the perianastomotic graft and proximal host whilst the other case has a relatively uniform cross section. The third case is nonplanar and characterized by a wide GPA resulting from the graft being constructed superficially from an in situ vein. In all three models the same peripheral resistance was imposed at the computational outflows of the distal and proximal host vessels and this condition, combined with the effect of the anastomotic geometry, has been observed to reasonably reproduce the in vivo flow split. By analyzing the flow fields we demonstrate how the local and global geometric characteristics influences the distribution of wall shear stress and the steady transport of fluid particles. Specifically, in vessels that have a global geometric characteristic we observe that the wall shear stress depends on large scale geometrical factors, e.g., the curvature and planarity of blood vessels. In contrast, the wall shear stress distribution and local mixing is significantly influenced by morphology and location of restrictions, particular when there is a shallow GPA. A combination of local and global effects are also possible as demonstrated in our third study of an anastomosis with a larger GPA. These relatively simple observations highlight the need to distinguish between local and global geometric influences for a given reconstruction. We further present the geometrical evolution of the anastomoses over a series of follow-up studies and observe how the lumen progresses towards the faster bulk flow of the velocity in the original geometry. This mechanism is consistent with the luminal changes in recirculation regions that experience low wall shear stress. In the shallow GPA anastomoses the proximal part of the native host vessel occludes or stenoses earlier than in the case with wide GPA. A potential contribution to this behavior is suggested by the stronger mixing that characterizes anastomoses with large GPA.     

CFD simulation of flow through heart: a perspective review

The heart is an organ which pumps blood around the body by contraction of muscular wall. There is a coupled system in the heart containing the motion of wall and the motion of blood fluid; both motions must be computed simultaneously, which make biological computational fluid dynamics (CFD) difficult. The wall of the heart is not rigid and hence proper boundary conditions are essential for CFD modelling. Fluid-wall interaction is very important for real CFD modelling. There are many assumptions for CFD simulation of the heart that make it far from a real model. A realistic fluid-structure interaction modelling the structure by the finite element method and the fluid flow by CFD use more realistic coupling algorithms. This type of method is very powerful to solve the complex properties of the cardiac structure and the sensitive interaction of fluid and structure. The final goal of heart modelling is to simulate the total heart function by integrating cardiac anatomy, electrical activation, mechanics, metabolism and fluid mechanics together, as in the computational framework.     

4D subject-specific inverse modeling of the chick embryonic heart outflow tract hemodynamics

Blood flow plays a critical role in regulating embryonic cardiac growth and development, with altered flow leading to congenital heart disease. Progress in the field, however, is hindered by a lack of quantification of hemodynamic conditions in the developing heart. In this study, we present a methodology to quantify blood flow dynamics in the embryonic heart using subject-specific computational fluid dynamics (CFD) models. While the methodology is general, we focused on a model of the chick embryonic heart outflow tract (OFT), which distally connects the heart to the arterial system, and is the region of origin of many congenital cardiac defects. Using structural and Doppler velocity data collected from optical coherence tomography, we generated 4D (\(\hbox {3D}\,+\,\hbox {time}\)) embryo-specific CFD models of the heart OFT. To replicate the blood flow dynamics over time during the cardiac cycle, we developed an iterative inverse-method optimization algorithm, which determines the CFD model boundary conditions such that differences between computed velocities and measured velocities at one point within the OFT lumen are minimized. Results from our developed CFD model agree with previously measured hemodynamics in the OFT. Further, computed velocities and measured velocities differ by \(<\)15 % at locations that were not used in the optimization, validating the model. The presented methodology can be used in quantifications of embryonic cardiac hemodynamics under normal and altered blood flow conditions, enabling an in-depth quantitative study of how blood flow influences cardiac development.