Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation

The oscillatory shear index (OSI) was developed based on the hypothesis that intimal hyperplasia was correlated with oscillatory shear stresses. However, the validity of the OSI was in question since the correlation between intimal thickness and the OSI at the side walls of the sinus in the Y-shaped model of the average human carotid bifurcation (Y-AHCB) was weak. The objectives of this paper are to examine whether the reason for the weak correlation lies in the deviation in geometry of Y-AHCB from real human carotid bifurcation, and whether this correlation is clearly improved in the tuning-fork-shaped model of the average human carotid bifurcation (TF-AHCB). The geometry of the TF-AHCB model was based on observation and statistical analysis of specimens from 74 cadavers. The flow fields in both models were studied and compared by using flow visualization methods under steady flow conditions and by using laser Doppler anemometer (LDA) under pulsatile flow conditions. The TF-shaped geometry leads to a more complex flow field than the Y-shaped geometry. This added complexity includes strengthened helical movements in the sinus, new flow separation zone, and directional changes in the secondary flow patterns. The results show that the OSI-values at the side walls of the sinus in the TF-shaped model were more than two times as large as those in the Y-shaped model. This study confirmed the stronger correlation between the OSI and intimal thickness in the tuning-fork geometry of human carotid bifurcation, and the TF-AHCB model is a significant improvement over the traditional Y-shaped model.     

Differential gene expression in primary and recurrent carotid stenosis

Apoptosis of the cellular components of complex atherosclerotic plaque may lead to plaque instability and rupture. In this study, five primary plaques and one recurrent fibrointimal lesion obtained from patients undergoing carotid endarterectomy for symptomatic carotid stenosis > or = 70% were analyzed by immunohistochemistry and cDNA microarray to identify gene expression patterns that may determine plaque susceptibility or resistance to apoptosis. Immunohistochemistry showed expression of active caspase 3, an effector of apoptosis, in macrophages and lymphocytes surrounding the lipid core, in smooth muscle cells in the fibrous cap, and media of primary plaques as well as in occasional smooth muscle cells in the recurrent lesion. Among the genes demonstrating increased expression in primary plaques were IGFR2, DR4, DAPK1, Bak, and ERK 1 and 2 and those showing decreased expression included the TNF receptors 1 and 2, akt1, and IGFBP3. When comparing the recurrent lesion to the normal tissue, the expression of 13 genes was decreased by 3-fold, including IGFBP2 and IGFBP3, and none were increased by more than 1.5-fold. The analysis of gene expression patterns in primary and recurrent stenotic lesions provides a powerful approach to identify the signaling pathways that alter cellular apoptotic patterns in such lesions.     

Numerical bifurcation analysis of the pattern formation in a cell based auxin transport model

Transport models of growth hormones can be used to reproduce the hormone accumulations that occur in plant organs. Mostly, these accumulation patterns are calculated using time step methods, even though only the resulting steady state patterns of the model are of interest. We examine the steady state solutions of the hormone transport model of Smith et al. (Proc Natl Acad Sci USA 103(5):1301–1306, 2006) for a one-dimensional row of plant cells. We search for the steady state solutions as a function of three of the model parameters by using numerical continuation methods and bifurcation analysis. These methods are more adequate for solving steady state problems than time step methods. We discuss a trivial solution where the concentrations of hormones are equal in all cells and examine its stability region. We identify two generic bifurcation scenarios through which the trivial solution loses its stability. The trivial solution becomes either a steady state pattern with regular spaced peaks or a pattern where the concentration is periodic in time.     

A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation

A finite element approximation of steady flow in a rigid three-dimensional model of the carotid artery bifurcation is presented. A Reynolds number of 640 and a flow division ratio of about 50/50, simulating systolic flow, was used. To limit the CPU- and I/O-times needed for solving the systems of equations, a mesh-generator was developed, which gives full control over the number of elements into which the bifurcation is divided. A mini-supercomputer, based on parallel and vector processing techniques, was used to solve the system of equations. The numerical results of axial and secondary flow compare favorably with those obtained from previously performed laser-Doppler velocity measurements. Also, the influence of the Reynolds number, the flow division ratio, and the bifurcation angle on axial and secondary flow in the carotid sinus were studied in the three-dimensional model. The influence of the interventions is limited to a relatively small variation in the region with reversed axial flow, more or less pronounced C-shaped axial velocity contours, and increasing or decreasing axial velocity maxima.     

Small-bubble transport and splitting dynamics in a symmetric bifurcation

Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.     

An experimental analysis of the flow field in a three-dimensional model of the human carotid artery bifurcation

Steady flow measurements were carried out in a rigid three-dimensional model of the human carotid artery bifurcation at a Reynolds number of 640 and a flow division ratio of 50/50. Both axial and secondary velocities were measured with a laser-Doppler anemometer. In the bulb opposite to the flow divider a zone with negative axial velocities was found with a maximal diameter of about 60% of the local diameter of the branch and a cross-sectional extent of about 25% of the local cross-sectional area. In the bulb the maximum axial velocity shifted towards the divider wall and at the end of the bulb an axial velocity plateau arose near the non-divider wall. Halfway through the bulb, secondary flow showed a vortex through which fluid flowed towards the divider wall near the bifurcation plane and back towards the non-divider wall near the upper walls.     

Turbulence detection in a stenosed artery bifurcation by numerical simulation of pulsatile blood flow using the low-Reynolds number turbulence model

The pulsatile blood flow in a partially blocked artery is significantly altered as the flow regime changes through the cardiac cycle. This paper reports on the application of a low-Reynolds turbulence model for computation of physiological pulsatile flow in a healthy and stenosed carotid artery bifurcation. The human carotid artery was chosen since it has received much attention because atherosclerotic lesions are frequently observed. The Wilcox low-Re k-omega turbulence model was used for the simulation since it has proven to be more accurate in describing transition from laminar to turbulent flow. Using the FIDAP finite element code a validation showed very good agreement between experimental and numerical results for a steady laminar to turbulent flow transition as reported in a previous publication by the same authors. Since no experimental or numerical results were available in the literature for a pulsatile and turbulent flow regime, a comparison between laminar and low-Re turbulent calculations was made to further validate the turbulence model. The results of this study showed a very good agreement for velocity profiles and wall shear stress values for this imposed pulsatile laminar flow regime. To explore further the medical aspect, the calculations showed that even in a healthy or non-stenosed artery, small instabilities could be found at least for a portion of the pulse cycle and in different sections. The 40% and 55% diameter reduction stenoses did not significantly change the turbulence characteristics. Further results showed that the presence of 75% stenoses changed the flow properties from laminar to turbulent flow for a good portion of the cardiac pulse. A full 3D simulation with this low-Re-turbulence model, coupled with Doppler ultrasound, can play a significant role in assessing the degree of stenosis for cardiac patients with mild conditions.     

Flow instability detected in ruptured versus unruptured cerebral aneurysms at the internal carotid artery

Flow instability has emerged as a new hemodynamic metric hypothesized to have potential value in assessing the rupture risk of cerebral aneurysms. However, diverse findings have been reported in the literature. In the present study, high-resolution hemodynamic simulations were performed retrospectively on 35 aneurysms (10 ruptured & 25 unruptured) located at the internal carotid artery (ICA). Simulated hemodynamic parameters were statistically compared between the ruptured and unruptured aneurysms, with emphasis on examining the correlation of flow instability with the status of aneurysm rupture. Pronounced flow instability was detected in 20% (2 out of 10) of the ruptured aneurysms, whereas in 44% (11 out of 25) of the unruptured aneurysms. Statistically, the flow instability metric (quantified by the temporally and spatially averaged fluctuating kinetic energy over the aneurysm sac) did not differ significantly between the ruptured and unruptured aneurysms. In contrast, low wall shear stress area (LSA) and pressure loss coefficient (PLC) exhibited significant correlations with the status of aneurysm rupture. In conclusion, the present study suggests that the presence of flow instability may not correlate closely with the status of aneurysm rupture, at least for ICA aneurysms. On the other hand, the retrospective nature of the study and the small sample size may have to some extent compromised the reliability of the conclusion, and therefore large-scale prospective studies would be needed to further address the issue.     

A numerical and experimental analysis of the flow field in a two-dimensional model of the human carotid artery bifurcation

Axial velocities were measured in an enlarged, two-dimensional, rigid model of the carotid artery bifurcation by means of a laser-Doppler anemometer, under both steady and unsteady flow conditions. Also a numerical model was developed, based on the finite element approximation of the Navier-Stokes and continuity equations. From this study it appeared that the numerically predicted velocities agree well with the experimentally obtained values. Besides, the bifurcation hardly influenced the upstream flow in the main branch (common carotid artery), high velocity gradients were observed at the divider walls of the daughter branches (internal and external carotid arteries) and large zones with reversed flow were present near the nondivider walls of these branches. For steady flow the maximal diameter of this zone at the entrance of the internal carotid artery (carotid sinus) was about 25% of the local diameter of this branch. For unsteady flow this zone was absent during the initial phase of flow acceleration and maximal at the end of flow deceleration with a maximal diameter of about 50% of the local diameter of the carotid sinus.     

Flow pattern visualization in a mimic anaerobic digester using CFD

Three-dimensional steady-state computational fluid dynamics (CFD) simulations were performed in mimic anaerobic digesters to visualize their flow pattern and obtain hydrodynamic parameters. The mixing in the digester was provided by sparging gas at three different flow rates. The gas phase was simulated with air and the liquid phase with water. The CFD results were first evaluated using experimental data obtained by computer automated radioactive particle tracking (CARPT). The simulation results in terms of overall flow pattern, location of circulation cells and stagnant regions, trends of liquid velocity profiles, and volume of dead zones agree reasonably well with the experimental data. CFD simulations were also performed on different digester configurations. The effects of changing draft tube size, clearance, and shape of the tank bottoms were calculated to evaluate the effect of digester design on its flow pattern. Changing the draft tube clearance and height had no influence on the flow pattern or dead regions volume. However, increasing the draft tube diameter or incorporating a conical bottom design helped in reducing the volume of the dead zones as compared to a flat-bottom digester. The simulations showed that the gas flow rate sparged by a single point (0.5 cm diameter) sparger does not have an appreciable effect on the flow pattern of the digesters at the range of gas flow rates used.     

Flow patterns and endothelial cell morphology in a simplified model of an artificial ventricle

The aim of this study was to delineate the flow patterns in a non-unidirectional flow field inside a ventricle-shaped cell culture chamber, and examine the resulting morphology and integrity of the endothelium in select regions of the monolayer. The chamber was perfused by pulsatile flow, and the coherent motion of the fluid was studied using flow visualization aided by image analysis. Four distinct flow patterns were discerned and examined: central jet, flow impingement, flow separation, and recirculating eddies. The influence of these patterns on endothelial cell morphology was assessed after 20 h of exposure to flow. There were no signs of damage to the endothelium in the jet region nor was there evidence of cell alignment with the flow. Yet, there were changes in cell morphology and cytoskeletal architecture as compared to control. By contrast, within the eddies where the flow was highly disturbed, there was apparent damage to the endothelium. Thus, exposure of cells to random velocity fluctuations in regions of quasi-static flow compromises the integrity of the monolayer. Identification of such sites and acquisition of the knowledge necessary to protect the cells from denudation will be valuable for the endothelialization efforts of cardiac prostheses.     

Implantation of a Carotid Cuff for Triggering Shear-stress Induced Atherosclerosis in Mice

It is widely accepted that alterations in vascular shear stress trigger the expression of inflammatory genes in endothelial cells and thereby induce atherosclerosis (reviewed in ¹ and ²). The role of shear stress has been extensively studied in vitro investigating the influence of flow dynamics on cultured endothelial cells ^1,3,4 and in vivo in larger animals and humans ^1,5,6,7,8. However, highly reproducible small animal models allowing systematic investigation of the influence of shear stress on plaque development are rare. Recently, Nam et al. ⁹ introduced a mouse model in which the ligation of branches of the carotid artery creates a region of low and oscillatory flow. Although this model causes endothelial dysfunction and rapid formation of atherosclerotic lesions in hyperlipidemic mice, it cannot be excluded that the observed inflammatory response is, at least in part, a consequence of endothelial and/or vessel damage due to ligation.In order to avoid such limitations, a shear stress modifying cuff has been developed based upon calculated fluid dynamics, whose cone shaped inner lumen was selected to create defined regions of low, high and oscillatory shear stress within the common carotid artery ¹⁰. By applying this model in Apolipoprotein E (ApoE) knockout mice fed a high cholesterol western type diet, vascular lesions develop upstream and downstream from the cuff. Their phenotype is correlated with the regional flow dynamics ¹¹ as confirmed by in vivo Magnetic Resonance Imaging (MRI) ¹²: Low and laminar shear stress upstream of the cuff causes the formation of extensive plaques of a more vulnerable phenotype, whereas oscillatory shear stress downstream of the cuff induces stable atherosclerotic lesions ¹¹. In those regions of high shear stress and high laminar flow within the cuff, typically no atherosclerotic plaques are observed.In conclusion, the shear stress-modifying cuff procedure is a reliable surgical approach to produce phenotypically different atherosclerotic lesions in ApoE-deficient mice.     

Computational fluid dynamics in abdominal aorta bifurcation: non-Newtonian versus Newtonian blood flow in a real case study

Hemodynamic in abdominal aorta bifurcation was investigated in a real case using computational fluid dynamics. A Newtonian and non-Newtonian (Walburn-Schneck) viscosity models were compared. The geometrical model was obtained by 3D reconstruction from CT-scan and hemodynamic parameters obtained by laser-Doppler. Blood was assumed incompressible fluid, laminar flow in transient regime and rigid vessel wall. Finite volume-based was used to study the velocity, pressure, wall shear stress (WSS) and viscosity throughout cardiac cycle. Results obtained with Walburn-Schneck’s model, during systole, present lower viscosity due to shear thinning behavior. Furthermore, there is a significant difference between the results obtained by the two models for a specific patient. During the systole, differences are more pronounced and are preferably located in the tortuous regions of the artery. Throughout the cardiac cycle, the WSS amplitude between the systole and diastole is greater for the Walburn-Schneck’s model than for the Newtonian model. However, the average viscosity along the artery is always greater for the non-Newtonian model, except in the systolic peak. The hemodynamic model is crucial to validate results obtained with CFD and to explore clinical potential.     

Flow field analysis in a compliant acinus replica model using particle image velocimetry (PIV)

Inhaled particles reaching the alveolar walls have the potential to cross the blood–gas barrier and enter the blood stream. Experimental evidence of pulmonary dosimetry, however, cannot be explained by current whole lung dosimetry models. Numerical and experimental studies shed some light on the mechanisms of particle transport, but realistic geometries have not been investigated. In this study, a three dimensional expanding model including two generations of respiratory bronchioles and five terminal alveolar sacs was created from a replica human lung cast. Flow visualization techniques were employed to quantify the fluid flow while utilizing streamlines to evaluate recirculation. Pathlines were plotted to track the fluid motion and estimate penetration depth of inhaled air. This study provides evidence that the two generations immediately proximal to the terminal alveolar sacs do not have recirculating eddies, even for intense breathing. Results of Peclet number calculations indicate that substantial convective motion is present in vivo for the case of deep breathing, which significantly increases particle penetration into the alveoli. However, particle diffusion remains the dominant mechanism of particle transport over convection, even for intense breathing because inhaled particles do not reach the alveolar wall in a single breath by convection alone. Examination of the velocity fields revealed significant uneven ventilation of the alveoli during a single breath, likely due to variations in size and location. This flow field data, obtained from replica model geometry with realistic breathing conditions, provides information to better understand fluid and particle behavior in the acinus region of the lung.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.     

Improvement and validation of a computational model of flow in the swirling well cell culture model

Effects of fluid dynamics on cells are often studied by growing the cells on the base of cylindrical wells or dishes that are swirled on the horizontal platform of an orbital shaker. The swirling culture medium applies a shear stress to the cells that varies in magnitude and directionality from the center to the edge of the vessel. Computational fluid dynamics methods are used to simulate the flow and hence calculate shear stresses at the base of the well. The shear characteristics at each radial location are then compared with cell behavior at the same position. Previous simulations have generally ignored effects of surface tension and wetting, and results have only occasionally been experimentally validated. We investigated whether such idealized simulations are sufficiently accurate, examining a commonly-used swirling well configuration. The breaking wave predicted by earlier simulations was not seen, and the edge-to-center difference in shear magnitude (but not directionality) almost disappeared, when surface tension and wetting were included. Optical measurements of fluid height and velocity agreed well only with the computational model that incorporated surface tension and wetting. These results demonstrate the importance of including accurate fluid properties in computational models of the swirling well method.     

Regeneration pattern analysis of Quercus Iiaotungensis in a temperate forest using two-dimensional wavelet analysis

This paper introduces the two-dimensional (2D) wavelet analysis as a general interrogative technique for the detection of spatial structure in lattice data. The 2D wavelet analysis detects components of hierarchical structure and displays the locational information of the components. Patches and gaps of different spatial scales in graphical presentation of wavelet coefficients can be linked to the local ecological processes that determine patterns at stand or landscape scales. Derived from the 2D wavelet transform function, the calculation of wavelet variance can reduce the four-dimensional data of wavelet coefficients to a two-dimensional wavelet variance function and quantify the contribution of the given scale to the overall pattern. We illustrate the use of the 2D wavelet analysis by analyzing two simulated patterns and identifying the regeneration pattern of the Quercus liaotungensis in a warm temperate forest in north China. Our results indicate that the recruitment of Q. liaotungensis occurs in an overlapping area between the patch of adult and canopy gap at scales of 45m×45m-70m×70 m and 20m×20m-30m×30m. The regeneration pattern of Q. liaotungensis can be mainly ascribed to a trade-off between two ecological processes: recruitment around parent trees and the physiological light requirements of seedlings and saplings. Our results provide a general portrayal of the regeneration pattern for the dispersal-limited and shade-intolerant Quercus species. We find that the two-dimensional wavelet analysis efficiently characterizes the scale-specific pattern of Q. liaotungensis at different life-history stages.     

Modeling evaluation of the fluid-dynamic microenvironment in tissue-engineered constructs: a micro-CT based model

Natural cartilage remodels both in vivo and in vitro in response to mechanical stresses, hence mechanical stimulation is believed to be a potential tool to modulate extra-cellular matrix synthesis in tissue-engineered cartilage. Fluid-induced shear is known to enhance chondrogenesis in engineered cartilage constructs. The quantification of the hydrodynamic environment is a condition required to study the biochemical response to shear of 3D engineered cell systems. We developed a computational model of culture medium flow through the microstructure of a porous scaffold, during direct- perfused culture. The 3D solid model of the scaffold micro-geometry was reconstructed from 250 micro-computed tomography (micro-CT) images. The results of the fluid dynamic simulations were analyzed at the central portions of the fluid domain, to avoid boundary effects. The average, median and mode shear stress values calculated at the scaffold walls were 3.48, 2.90, and 2.45 mPa respectively, at a flow rate of 0.5 cm(3)/min, perfused through a 15 mm diameter scaffold, at an inlet fluid velocity of 53 microm/s. These results were compared to results estimated using a simplified micro-scale model and to results estimated using an analytical macro-scale porous model. The predictions given by the CT-based model are being used in conjunction with an experimental bioreactor model, in order to quantify the effects of fluid-dynamic shear on the growth modulation of tissue-engineered cartilage constructs, to potentially enhance tissue growth in vitro.