A numerical simulation of steady flow fields in a bypass tube.

Steady flow in a complete by-pass tube was simulated numerically. The study was to consider a complete flow field, which included both the by-pass and the host tubes. The changes of the hemodynamics were investigated with three parameters: the inlet flow Reynolds number (Re), anastomotic angle (alpha) and the position of the occlusion in the host tube. The baseline flow field was set up with Re=200, alpha=45 degrees and the centered position of occlusion. The parametric study was then conducted on combination of Re=100, 200, 400, alpha=35 degrees, 45 degrees, 60 degrees, 75 degrees, 90 degrees and three occlusion positions: left, center and right. It was found that in the baseline case, large slow/recirculation flows could be seen in the host tube both upstream and downstream of the occlusion. The separation points were on the opposite walls to the junctions. Recirculation zones were also found near the toe and in the proximal outer wall of the by-pass tube. Their sizes were about one diameter of the tube or smaller. In some cases, pairing vortices could be seen in the host tube upstream of the occlusion. The shear rate distribution associated with the flow fields was presented. The flow pattern obtained was agreeable to those observed experimentally by other investigators. The difference of the flow fields between a complete bypass and simple anastomosis was discussed. The present numerical code provides a preliminary simulation/design tool for bypass graft flows.     

Fluid flow structure in arterial bypass anastomosis

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

3-D numerical simulation of blood flow through models of the human aorta

A Spiral Computerized Tomography (CT) scan of the aorta were obtained from a single subject and three model variations were examined. Computational fluid dynamics modeling of all three models showed variations in the velocity contours along the aortic arch with differences in the boundary layer growth and recirculation regions. Further down-stream, all three models showed very similar velocity profiles during maximum velocity with differences occurring in the decelerating part of the pulse. Flow patterns obtained from transient 3-D computational fluid dynamics are influenced by different reconstruction methods and the pulsatility of the flow. Caution is required when analyzing models based on CT scans.     

Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis

Numerical simulations of pulsatile blood flow in straight tube stenosis models were performed to investigate the poststenotic flow phenomena. In this study, three axisymmetrical and three asymmetrical stenosis models with area reduction of 25%, 50% and 75% were constructed. A measured human common carotid artery blood flow waveform was used as the upstream flow condition which has a mean Reynold's number of 300. All calculations were performed with high spatial and temporal resolutions. Flow features such as velocity profiles, flow separation zone (FSZ), and wall shear stress (WSS) distributions in the poststenotic region for all models are presented. The results have demonstrated that the formation and development of FSZs in the poststenotic region are very complex, especially in the flow deceleration phase. In axisymmetric stenoses the poststenotic flow is more sensitive to changes in the degree of stenosis than in asymmetric models. For severe stenoses, the stenosis influence length is shorter in asymmetrical models than in axisymmetrical cases. WSS oscillations (between positive and negative values) have been observed at various downstream locations in some models. The amplitude of the oscillation depends strongly on the axial location and the degree of stenosis.     

Molecular simulation of realistic membrane models of alkylated PEEK membranes

Atomistic molecular modelling has proven to be a useful tool for the investigation of transport properties of small gas molecules in polymer membrane matrices. The quality of the predictions of these properties based on molecular simulation depends principally on the quality of the membrane model. The predicted gas transport properties of small gas molecules in the same glassy polymer membrane show often a large scatter in gas diffusion and solubility simulated values. In order to reduce the scatter in predicted gas transport properties in glassy polymer membranes, numerical analysis of structural features of the membrane model is used for pre-selecting only the realistic ones for further simulations using transition-state theory (TST) approach. Simulation results of gas solubility and diffusion in alkylated poly-ether–ether–ketone (PEEK) membranes will illustrate the approach.     

Comparative analysis of realistic CT-scan and simplified human airway models in airflow simulation

Efforts to model the human upper respiratory system have undergone many phases. Geometrical proximity to the realistic shape has been the subject of many research projects. In this study, three different geometries of the trachea and main bronchus were modelled, which were reconstructed from computed tomography (CT) scan images. The geometrical variations were named realistic, simplified and oversimplified. Realistic refers to the lifelike image taken from digital imaging and communications in medicine format CT scan images, simplified refers to the reconstructed image based on natural images without realistic details pertaining to the rough surfaces, and oversimplified describes the straight wall geometry of the airway. The characteristics of steady state flows with different flow rates were investigated, simulating three varied physical activities and passing through each model. The results agree with previous studies where simplified models are sufficient for providing comparable results for airflow in human airways. This work further suggests that, under most exercise conditions, the idealised oversimplified model is not favourable for simulating either airflow regimes or airflow with particle depositions. However, in terms of immediate analysis for the prediction of abnormalities of various dimensions of human airways, the oversimplified techniques may be used.     

Computational model of blood flow in the aorto-coronary bypass graft

Background

Coronary artery bypass grafting surgery is an effective treatment modality for patients with severe coronary artery disease. The conduits used during the surgery include both the arterial and venous conduits. Long- term graft patency rate for the internal mammary arterial graft is superior, but the same is not true for the saphenous vein grafts. At 10 years, more than 50% of the vein grafts would have occluded and many of them are diseased. Why do the saphenous vein grafts fail the test of time? Many causes have been proposed for saphenous graft failure. Some are non-modifiable and the rest are modifiable. Non-modifiable causes include different histological structure of the vein compared to artery, size disparity between coronary artery and saphenous vein. However, researches are more interested in the modifiable causes, such as graft flow dynamics and wall shear stress distribution at the anastomotic sites. Formation of intimal hyperplasia at the anastomotic junction has been implicated as the root cause of long- term graft failure.Many researchers have analyzed the complex flow patterns in the distal sapheno-coronary anastomotic region, using various simulated model in an attempt to explain the site of preferential intimal hyperplasia based on the flow disturbances and differential wall stress distribution. In this paper, the geometrical bypass models (aorto-left coronary bypass graft model and aorto-right coronary bypass graft model) are based on real-life situations. In our models, the dimensions of the aorta, saphenous vein and the coronary artery simulate the actual dimensions at surgery. Both the proximal and distal anastomoses are considered at the same time, and we also take into the consideration the cross-sectional shape change of the venous conduit from circular to elliptical. Contrary to previous works, we have carried out computational fluid dynamics (CFD) study in the entire aorta-graft-perfused artery domain. The results reported here focus on (i) the complex flow patterns both at the proximal and distal anastomotic sites, and (ii) the wall shear stress distribution, which is an important factor that contributes to graft patency.

Methods

The three-dimensional coronary bypass models of the aorto-right coronary bypass and the aorto-left coronary bypass systems are constructed using computational fluid-dynamics software (Fluent 6.0.1). To have a better understanding of the flow dynamics at specific time instants of the cardiac cycle, quasi-steady flow simulations are performed, using a finite-volume approach. The data input to the models are the physiological measurements of flow-rates at (i) the aortic entrance, (ii) the ascending aorta, (iii) the left coronary artery, and (iv) the right coronary artery.

Results

The flow field and the wall shear stress are calculated throughout the cycle, but reported in this paper at two different instants of the cardiac cycle, one at the onset of ejection and the other during mid-diastole for both the right and left aorto-coronary bypass graft models. Plots of velocity-vector and the wall shear stress distributions are displayed in the aorto-graft-coronary arterial flow-field domain. We have shown (i) how the blocked coronary artery is being perfused in systole and diastole, (ii) the flow patterns at the two anastomotic junctions, proximal and distal anastomotic sites, and (iii) the shear stress distributions and their associations with arterial disease.

Conclusion

The computed results have revealed that (i) maximum perfusion of the occluded artery occurs during mid-diastole, and (ii) the maximum wall shear-stress variation is observed around the distal anastomotic region. These results can enable the clinicians to have a better understanding of vein graft disease, and hopefully we can offer a solution to alleviate or delay the occurrence of vein graft disease.

     

PIV-measured versus CFD-predicted flow dynamics in anatomically realistic cerebral aneurysm models

Computational fluid dynamics (CFD) modeling of nominally patient-specific cerebral aneurysms is increasingly being used as a research tool to further understand the development, prognosis, and treatment of brain aneurysms. We have previously developed virtual angiography to indirectly validate CFD-predicted gross flow dynamics against the routinely acquired digital subtraction angiograms. Toward a more direct validation, here we compare detailed, CFD-predicted velocity fields against those measured using particle imaging velocimetry (PIV). Two anatomically realistic flow-through phantoms, one a giant internal carotid artery (ICA) aneurysm and the other a basilar artery (BA) tip aneurysm, were constructed of a clear silicone elastomer. The phantoms were placed within a computer-controlled flow loop, programed with representative flow rate waveforms. PIV images were collected on several anterior-posterior (AP) and lateral (LAT) planes. CFD simulations were then carried out using a well-validated, in-house solver, based on micro-CT reconstructions of the geometries of the flow-through phantoms and inlet/outlet boundary conditions derived from flow rates measured during the PIV experiments. PIV and CFD results from the central AP plane of the ICA aneurysm showed a large stable vortex throughout the cardiac cycle. Complex vortex dynamics, captured by PIV and CFD, persisted throughout the cardiac cycle on the central LAT plane. Velocity vector fields showed good overall agreement. For the BA, aneurysm agreement was more compelling, with both PIV and CFD similarly resolving the dynamics of counter-rotating vortices on both AP and LAT planes. Despite the imposition of periodic flow boundary conditions for the CFD simulations, cycle-to-cycle fluctuations were evident in the BA aneurysm simulations, which agreed well, in terms of both amplitudes and spatial distributions, with cycle-to-cycle fluctuations measured by PIV in the same geometry. The overall good agreement between PIV and CFD suggests that CFD can reliably predict the details of the intra-aneurysmal flow dynamics observed in anatomically realistic in vitro models. Nevertheless, given the various modeling assumptions, this does not prove that they are mimicking the actual in vivo hemodynamics, and so validations against in vivo data are encouraged whenever possible.     

Simulation of flow through a Miller cuff bypass graft

Unnatural temporal and spatial distributions of wall shear stress in the anastomosis of distal bypass grafts have been identified as possible factors in the development of anastomotic intimal hyperplasia in these grafts. Distal bypass graft anastomoses with an autologus vein cuff (a Miller cuff) interposed between the graft and artery have been shown to alleviate the effects of intimal hyperplasia. In this study, pulsatile flow through models of a standard end-to-side anastomosis and a Miller cuff anastomosis are computed and the resulting wall shear stress and pressure distributions analysed. The results are inconclusive, and could be taken to suggest that the unnatural distributions of shear stress that do occur along the anastomosis floor may not be particularly important in the development of intimal hyperplasia. However, it seems more likely that the positive effects of the biological and material properties of the vein cuff, which are not considered in this study, somehow outweigh the negative effects of the shear stress distributions predicted to occur on the floor of the Miller-cuff graft.     

Numerical simulation of wall shear stress conditions and platelet localization in realistic end-to-side arterial anastomoses

Research studies over the last three decades have established that hemodynamic interactions with the vascular surface as well as surgical injury are inciting mechanisms capable of eliciting distal anastomotic intimal hyperplasia (IH) and ultimate bypass graft failure. While abnormal wall shear stress (WSS) conditions have been widely shown to affect vascular biology and arterial wall self-regulation, the near-wall localization of critical blood particles by convection and diffusion may also play a significant role in IH development. It is hypothesized that locations of elevated platelet interactions with reactive or activated vascular surfaces, due to injury or endothelial dysfunction, are highly susceptible to IH initialization and progression. In an effort to assess the potential role of platelet-wall interactions, experimentally validated particle-hemodynamic simulations have been conducted for two commonly implemented end-to-side anastomotic configurations, with and without proximal outflow. Specifically, sites of significant particle interactions with the vascular surface have been identified by a novel near-wall residence time (NWRT) model for platelets, which includes shear stress-based factors for platelet activation as well as endothelial cell expression of thrombogenic and anti-thrombogenic compounds. Results indicate that the composite NWRT model for platelet-wall interactions effectively captures a reported shift in significant IH formation from the arterial floor of a relatively high-angle (30 deg) graft with no proximal outflow to the graft hood of a low-angle graft (10 deg) with 20% proximal outflow. In contrast, other WSS-based hemodynamic parameters did not identify the observed system-dependent shift in IH formation. However, large variations in WSS-vector magnitude and direction, as encapsulated by the WSS-gradient and WSS-angle-gradient parameters, were consistently observed along the IH-prone suture-line region. Of the multiple hemodynamic factors capable of eliciting a hyperplastic response at the cellular level, results of this study indicate the potential significance of platelet-wall interactions coinciding with regions of low WSS in the development of IH.     

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.     

Superoxide dismutase activity and expression in human venous and arterial bypass graft vessels.

Venous bypass grafts are more prone to accelerated atherosclerosis than arterial grafts, which is partly related to increased oxidative stress and diminished nitric oxide bioavailability. In veins superoxide production is dependent primarily on nox2 NAD(P)H oxidase expression, while in arteries nox4 appears to play an important role. This may in part explain differences in susceptibility to graft failure. Net levels of oxidative stress are however determined in parallel by the production as well as by degradation of free radicals (eg. by superoxide dismutases, catalases, thioredoxins etc). The differences in superoxide dismutase (SOD) expression and activity in human bypass conduit vessels remain unclear. Accordingly, we aimed to compare SOD activity and protein levels as well as its functional effects on superoxide production in segments of human internal mammary arteries (IMA) and saphenous veins (HSV) from patients undergoing bypass graft surgery (n=24). SOD activity was assessed by inhibition of pyrogallol autoxidation, Cu-Zn SOD and Mn SOD protein levels were studied by immunoblotting. Basal superoxide release was detected by lucigenin (5 microM) enhanced chemiluminescence. Total SOD activity did not differ significantly between HSV and IMA. Similarly, no difference was observed in SOD activity in the presence of KCN (Mn-SOD). Human bypass conduit vessels show amounts of Cu-Zn SOD or Mn-SOD protein levels. In both HSV and IMA segments superoxide production was more than doubled in the presence of SOD inhibitor-DETC. CONCLUSIONS: These studies suggest that the differences in oxidative stress between human arteries and veins are unlikely to be caused by SOD activity. However SOD plays and important role in amelioration of oxidative stress in both types of vessels.     

Computer simulation of arterial flow with applications to arterial and aortic stenoses

A computer model for simulating pressure and flow propagation in the human arterial system is developed. The model is based on the one-dimensional flow equations and includes nonlinearities arising from geometry and material properties. Fifty-five arterial segments, representing the various major arteries, are combined to form the model of the arterial system. Particular attention is paid to the development of peripheral pressure and flow pulses under normal flow conditions and under conditions of arterial and aortic stenoses. Results show that the presence of severe arterial stenoses significantly affects the nature of the distal pressure and flow pulses. Aortic stenoses also have a profound effect on central and peripheral pressure pulse formation. Comparison with the published experimental data suggests that the model is capable of simulating arterial flow under normal flow conditions as well as conditions of stenotic obstructions in a satisfactory manner.     

Three-dimensional numerical simulations of flow through a stenosed coronary bypass

This work analyzes the flow patterns at the anastomosis of a stenosed coronary bypass. Three-dimensional numerical simulations are performed using a finite elements method. We consider a geometrical model of the host coronary artery with and without a 75% severity stenosis for three different locations from the anastomosis. The flow features - velocity profiles, secondary motions and wall shear stresses - are compared for different configurations of the flow rate and of the distance of the anastomosis from the site of occlusion (called distance of grafting). The combination of the junction flow effects - counter rotating vortices - with the stenosis effects - confined jet flow - is particularly important when the distance of grafting is short. Given that the residual flow issued from the pathologic stenosis being non-negligible after two weeks grafting, models without stenosis cannot predict the evolution of the wall shear stress in the vicinity of the anastomosis.     

Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation

The pulsatile flow in an anatomically realistic compliant human carotid bifurcation was simulated numerically. Pressure and mass flow waveforms in the carotid arteries were obtained from an individual subject using non-invasive techniques. The geometry of the computational model was reconstructed from magnetic resonance angiograms. Maps of time-average wall shear stress, contours of velocity in the flow field as well as wall movement and tensile stress on the arterial wall are all presented. Inconsistent with previous findings from idealised geometry models, flow in the carotid sinus is dominated by a strong helical flow accompanied by a single secondary vortex motion. This type of flow is induced primarily by the asymmetry and curvature of the in vivo geometry. Flow simulations have been carried out under the rigid wall assumption and for the compliant wall, respectively. Comparison of the results demonstrates the quantitative influence of the vessel wall motion. Generally there is a reduction in the magnitude of wall shear stress, with its degree depending on location and phase of the cardiac cycle. The region of slow or reversed flow was greater, in both spatial and temporal terms in the compliant model, but the global characteristics of the flow and stress patterns remain unchanged. The analysis of mechanical stresses on the vessel surface shows a complicated stress field. Stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb. These are also regions of low wall shear stress. The comparison of computed and measured wall movement generally shows good agreement.     

Direct numerical simulation of transitional flow in a stenosed carotid bifurcation

The blood flow dynamics of a stenosed, subject-specific, carotid bifurcation were numerically simulated using the spectral element method. Pulsatile inlet conditions were based on in vivo color Doppler ultrasound measurements of blood velocity. The results demonstrated the transitional or weakly turbulent state of the blood flow, which featured rapid velocity and pressure fluctuations in the post-stenotic region of the internal carotid artery (ICA) during systole and laminar flow during diastole. High-frequency vortex shedding was greatest downstream of the stenosis during the deceleration phase of systole. Velocity fluctuations had a frequency within the audible range of 100-300Hz. Instantaneous wall shear stress (WSS) within the stenosis was relatively high during systole ( approximately 25-45Pa) compared to that in a healthy carotid. In addition, high spatial gradients of WSS were present due to flow separation on the inner wall. Oscillatory flow reversal and low pressure were observed distal to the stenosis in the ICA. This study predicts the complex flow field, the turbulence levels and the distribution of the biomechanical stresses present in vivo within a stenosed carotid artery.     

Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm

In experiments turbulence has previously been shown to occur in intracranial aneurysms. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulation in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, before relaminarization occurred during diastole. The turbulent structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5Pa. The recorded frequencies were predominantly in the range of 1-500Hz. The current study confirms, through properly resolved CFD simulations that turbulence can occur in intracranial aneurysms.