Xiao Yun Xu

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.

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 Reynolds 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.

Inter-individual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans

Fluid shear stress and mechanical wall stress may play a role in the formation of early atherosclerotic lesions, but these quantities are difficult to measure in vivo. Our objective was to quantify these parameters in normal subjects in a clinical setting, and to define regions of low wall shear stress and high mechanical stress. The right carotid bifurcations of five healthy male volunteers were investigated using a novel non-invasive technique which integrates magnetic resonance angiography, ultrasonography, tonometry and state-of-the-art computational fluid dynamics and solid mechanics models. Significant inter-subject variations in patterns as well as magnitude of wall shear stress and mechanical stress were found. In spite of individual variabilities, this study revealed that some regions of the artery wall are exposed simultaneously to low wall shear stress and high mechanical stress and that these regions correspond to areas where atherosclerotic plaque develops. The coexistence of regions of low wall shear stress and high tensile stress may be an important determinant of the formation of atheroma in human arteries.

Modelling of flow and wall behaviour in a mildly stenosed tube

In the present computational analysis, pulsatile flow and vessel wall behaviour in a simplified model of a stenosed vessel were investigated. Geometry of a 45% axisymmetrically stenosed (by area) cylindrical tube and a sinusoidal inflow waveform were simulated, with the fluid being assumed to be incompressible and Newtonian. The vessel wall was treated as a thick-walled, incompressible and isotropic material with uniform mechanical properties across the normal as well as the constricted segment. The study of fluid flow and wall motion was initially carried out separately using two commercial codes CFX4.2 and ABAQUS7 respectively. Their combined effects and interactions were later investigated through an iteratively coupled algorithm. Model validations on the rigid-wall fluid and static no-flow solid models were satisfactory, with Root Mean Square deviations of around 7% in centreline axial velocity between the prediction and measurement values for the rigid wall stenosis model, and 5% in circumferential stress for a cylindrical tube model under static loading when compared with the analytical solution. Results on velocity profiles, wall shear stress, intramural strain and stress for the rigid and compliant cases were all presented. Comparison between the rigid and compliant models revealed that, the flow separation layer distal to the stenosis was thicker and longer, and wall shear stress was slightly lower in the compliant model by less than 7.2%. Results obtained from the static wall model (with uniform pressure loading) and coupled fluid/wall interaction modelling of pulsatile flow showed qualitatively similar wall strain and stress patterns but considerable differences in magnitude. The radial and axial stresses were reduced by 31 and 8%, while the circumferential stress was increased by 13% due to the presence of pulsatile flow. Under the flow and structural conditions investigated, the effects of wall compliance were small, and did not change the flow and solid behaviours qualitatively in this case.

Numerical study of blood flow in an anatomically realistic aorto‐iliac bifurcation generated from MRI data

Magnetic resonance imaging and computational fluid dynamics (CFD) have been used in combination to simulate flow patterns at the human aorto‐iliac bifurcation. Vascular anatomy was reconstructed from stacked two‐dimensional (2D) time‐of‐flight images, and revealed asymmetric, nonplanar geometry with curvature in the abdominal aorta and right iliac artery. The left iliac artery was straight and exhibited a smaller take off angle than the right iliac artery. The anatomical reconstruction was used to generate a computational mesh and obtain CFD predictions of flow and wall shear stress (WSS) within the region of interest. The dynamic boundary conditions necessary were specified by 2D cine phase contrast measurements of velocity profiles in each component vessel. Predicted flow patterns were in good quantitative agreement with experiment and demonstrated major differences in WSS distributions between the iliac arteries. This noninvasive approach has considerable potential to evaluate local geometries and WSS as risk factors for arterial disease in individual subjects. Magn Reson Med 43:565–576, 2000.

Analysis of Flow Patterns in a Patient-Specific Aortic Dissection Model

Aortic dissection is the most common acute catastrophic event affecting the thoracic aorta. The majority of patients presenting with an uncomplicated type B dissection are treated medically, but 25% of these patients develop subsequent aneurysmal dilatation of the thoracic aorta. This study aimed at gaining more detailed knowledge of the flow phenomena associated with this condition. Morphological features and flow patterns in a dissected aortic segment of a presurgery type B dissection patient were analyzed based on computed tomography images acquired from the patient. Computational simulations of blood flow in the patient-specific model were performed by employing a correlation-based transitional version of Menters hybrid k-epsilon/k-omega shear stress transport turbulence model implemented in ANSYS CFX 11. Our results show that the dissected aorta is dominated by locally highly disturbed, and possibly turbulent, flow with strong recirculation. A significant proportion (about 80%) of the aortic flow enters the false lumen, which may further increase the dilatation of the aorta. High values of wall shear stress have been found around the tear on the true lumen wall, perhaps increasing the likelihood of expanding the tear. Turbulence intensity in the tear region reaches a maximum of 70% at midsystolic deceleration phase. Incorporating the non-Newtonian behavior of blood into the same transitional flow model has yielded a slightly lower peak wall shear stress and higher maximum turbulence intensity without causing discernible changes to the distribution patterns. Comparisons between the laminar and turbulent flow simulations show a qualitatively similar distribution of wall shear stress but a significantly higher magnitude with the transitional turbulence model.

The Influence of Inflow Boundary Conditions on Intra Left Ventricle Flow Predictions

The combination of computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) offers a promising tool that enables the prediction of blood flow patterns in subject-specific cardiovascular models. The influence of the model geometry on the accuracy of the simulation is well recognized. This paper addresses the impact of different boundary conditions on subject-specific simulations of left ventricular (LV) flow. A novel hybrid method for prescribing effective inflow boundary conditions in the mitral valve plane has been developed. The detailed quantitative results highlight the strengths as well as the potential pitfalls of the approach.

Comparative study of magnetic resonance imaging and image-based computational fluid dynamics for quantification of pulsatile flow in a carotid bifurcation phantom.

AbstractA combined magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modeling study was carried out for pulsatile flow in a carotid bifurcation phantom. The aim of the study was to quantify differences in flow patterns between MRI measurement and MRI-based CFD simulations and to further explore the potential for in vivo applications. The computational model was reconstructed from high resolution magnetic resonance (MR) scans. Velocities derived from phase-contrast MR measurements were used as boundary conditions for the CFD calculation. Detailed comparisons of velocity patterns were made between the CFD results and MRI measurements. Good agreement was achieved for the main velocity component in both well-behaved flow (in the common carotid) and disturbed region (in the carotid sinus). Comparison of in-plane velocity vectors showed less satisfactory consistency and revealed that the MR measurements obtained were inadequate to depict the secondary flow pattern as expected. It can be concluded that the combined MRI/CFD is expected to provide more reliable information about the full three-dimensional velocity field.

Subject-specific computational simulation of left ventricular flow based on magnetic resonance imaging

A detailed investigation of left ventricle (LV) flow patterns could improve our understanding of the function of the heart and provide further insight into the mechanisms of heart failure. This study presents patient-specific modelling with magnetic resonance imaging (MRI) to investigate LV blood flow patterns in normal subjects. In the study, the prescribed LV wall movements based on the MRI measurements drove the blood flow in and out of the LV in computational fluid dynamics simulation. For the six subjects studied, the simulated LV flow swirls towards the aortic valve and is ejected into the ascending aorta with a vertical flow pattern that follows the left-hand rule. In diastole, the inflow adopts a reasonably straight route (with no significant secondary flow) towards the apex in the rapid filling phase with slight variations in the jet direction between different cases. When the jet reaches about two thirds of the distance from the inflow plane to the apex, the blood flow starts to change direction and swirls towards the apex. In the more slowly filling phase, a centrally located jet is evident with vortices located on both sides of the jet on an anterior—posterior plane that passes through the mitral and aortic valves. In the inferior—superior plane, a main vortex appears for most of the cases in which an anticlockwise vortex appears for three cases and a clockwise vortex occurs for one case. The simulated flow patterns agree well qualitatively with MRI-measured flow fields.

Image-based carotid flow reconstruction: a comparison between MRI and ultrasound.

Atherosclerosis is a major cause of morbidity and mortality. Its apparent link with wall shear stress (WSS) has led to considerable interest in the in vivo estimation of WSS. Determining WSS by combining medical images with computational fluid dynamics (CFD) simulations can be performed both with magnetic resonance imaging (MRI) and three-dimensional ultrasound (3DUS). This study compares predicted 3D flow patterns based on black blood MRI and 3DUS. Velocity fields in the carotid arteries of nine subjects have been reconstructed, and the haemodynamic wall parameters WSS, oscillatory shear index (OSI), WSS gradients (WSSG) and angle gradients (WSSAG) were compared between the two imaging techniques. There was a good qualitative agreement between results derived from MRI and 3DUS (average correlation strength above 0.60). The root mean square error between haemodynamic wall parameters was comparable to the range of the expected variability of each imaging technique (WSS: 0.411 N m(-2); OSI: 0.048; temporal WSSG: 150 N s(-1) m(-2); spatial WSSG: 2.29 N m(-3); WSSAG: 87.6 rad m(-1)). In conclusion, MRI and 3DUS are capable of providing haemodynamic parameters when combined with CFD, and the predictions are in most cases qualitatively and quantitatively similar. The relatively high cost of MRI and continuing improvement in ultrasound favour US to MRI for future haemodynamic studies of superficial arteries.