Bifurcation Geometry Research Articles

Wall shear rate distribution in an abdominal aortic bifurcation model: effects of vessel compliance and phase angle between pressure and flow waveforms.

The goal of this study was to determine how vessel compliance (wall motion) and the phase angle between pressure and flow waves (impedance phase angle) affect the wall shear rate distribution in an atherogenic bifurcation geometry under sinusoidal flow conditions. Both rigid and elastic models replicating the human abdominal aortic bifurcation were fabricated and the wall shear rate distribution in the median plane of the bifurcation was determined using the photochronic flow visualization method. In the elastic model, three phase angle conditions were simulated (+12, -17, -61 deg), and the results compared with those obtained in a similar rigid model. The study indicates a very low (magnitude close to zero) and oscillatory wall shear rate zone within 1.5 cm distal to the curvature site on the outer (lateral) wall. In this low shear rate zone, unsteadiness (pulsatility) of the flow greatly reduces the mean (time-averaged) wall shear rate level. Vessel wall motion reduces the wall shear rate amplitude (time-varying component) up to 46 percent depending on the location and phase angle in the model. The mean wall shear rate is less influenced by the wall motion, but is reduced significantly in the low shear region (within 1.5 cm distal to the curvature site on the outer wall), thus rendering the wall shear rate waveform more oscillatory and making the site appear more atherogenic. The effect of the phase angle is most noteworthy on the inner wall close to the flow divider tip where the mean and amplitude of wall shear rate are 31 and 23 percent lower, respectively, at the phase angle of -17 deg than at -61 deg. However, the characteristics of the wall shear rate distribution in the low shear rate zone on the outer wall that are believed to influence localization of atherosclerotic disease, such as the mean wall shear rate level, oscillation in the wall shear rate waveform, and the length of the low and oscillatory wall shear rate zone, are similar for the three phase angles considered. The study also showed a large spatial variation of the phase angle between the wall shear stress waveform and the circumferential stress waveform (hoop stress due to radial artery expansion in response to pressure variations) near the bifurcation (up to 70 deg). The two stresses became more out of phase in the low mean shear rate zone on the outer wall (wall shear stress wave leading hoop stress wave as much as 125 deg at the pressure-flow phase angle of -61 deg) and were significantly influenced by the impedance phase angle.

Influence of the Geometry of the Left Main Coronary Artery Bifurcation on the Distribution of Sudanophilia in the Daughter Vessels

The proximal portions of the left anterior descending (LAD) and left circumflex (LCx) coronary arteries are among the sites most predisposed to atherosclerotic disease. This predisposition might be a consequence of their location immediately distal to the left main (LM) coronary artery bifurcation, which may increase the susceptibility of these segments by promoting an adverse fluid dynamic environment within them. The detailed geometry of the bifurcation influences this environment and would therefore affect the susceptibility of the proximal daughter vessels to disease. This hypothesis was tested by examination of the relationship between the geometry of the LM bifurcation and the distribution of sudanophilia in the proximal portions of the LAD and LCx. The geometric parameters at the LM bifurcation, including all three angles and LM length, were obtained from multiangle photographs of 17 vascular casts by use of objective computer-based algorithms. A robust index, the relative proximal involvement (RPI), was developed to measure the localization of disease to the proximal portions of the daughter vessels. The RPI of the LAD segment correlated best with an interaction term that included the planarity of the LM bifurcation and the LCx-LAD branch angle (P = .013). In addition to supporting the concept of geometric risk factors, these observations also suggest that interactions between the hemodynamic influences of multiple geometric variables may play a role in the mediation of tissue susceptibility by geometric factors.

An analysis of pulsatile flow in a model aortic bifurcation

An appropriate geometry of the model aortic bifurcation in the presence of stenosis is developed in order to analyse the flow phenomenon in the bifurcated aorta owing to a pulsatile pressure gradient. The flow in this geometry is determined by the branching of the aorta and the existence of a reverse flow area in the daughter artery. The present analysis incorporates the arterial wall motion and its effect on local fluid mechanics. From the computational results one may disclose that the non-Newtonian rheology of blood does not change the flow patterns in the parent aorta, but their is a drastic change in their daughter artery, which in turn causes an appreciable increase in the shear stress on both the parent and its daughter arteries. The present geometry bears the potential for a better understanding of the flow characteristics in daughter arteries where a stationary zone is located near the outer wall and a flow separation in the inner wall vicinity. The agreement between the present results and the existing ones is found to be quite satisfactory.

Effects of particle concentration on the partitioning of suspensions at small divergent bifurcations.

Experimental results are reported for the low Reynolds number flow of a suspension of spherical particles through a divergent capillary bifurcation consisting of a straight tube of circular cross-section that splits to form two tubes of equal diameter. The partitioning of particles between the downstream branches of the bifurcation is measured as a fraction of the partitioning of total volume (particles + suspending fluid) between the branches. Two bifurcation geometries are examined: a symmetric Y-shaped bifurcation and a nonsymmetric T-shaped bifurcation. This experiment focuses on the role of hydrodynamic interactions between particles on the partitioning of particles at the bifurcation. The particle diameter, made dimensionless with respect to the diameter of the branch tubes, ranges from 0.4 to 0.8. Results show that hydrodynamic interactions among the particles are significant at the bifurcation, even for conditions where interactions are unimportant in the straight branches away from the bifurcation. As a result of hydrodynamic interactions among particles at the bifurcation, the partitioning of particles between the branches is affected for particle volume fractions as small as 2 percent. The experimental results show that the effect of particle volume fraction is to diminish the inhomogeneity of particle partitioning at the bifurcation. However, the magnitude of this effect depends strongly on the overall shape of the bifurcation geometry, and, in particular on the angles between the branches.

Numerical simulation of flows of non-Newtonian fluids in the stenotic and bifurcated tubes

Steady flows of Newtonian and non-Newtonian fluids in the stenotic and bifurcated tubes are numerically simulated. Four rheologically different fluids such as water, aqueous sugar solution, aqueous Carbopol solution and blood are selected for the namerical simulation and the modified power-law model is used for the numerical simulation of non-Newtonian fluids in the stenotic and bifurcated tubes. Apparent viscosity of a non-Newtonian fluid in the modified power-law model is expressed as a function of the shear rate. Flows in the circular tube with sudden contraction-sudden expansion and gradual contraction-gradual expansion are studied numerically. Analyses in the stenotic tubes are concentrated on the effects of rheological properties, the stenotic geometry and Reynolds number. Flow characteristics of Carbopol solution in the stenotic tubes are compared with those of blood. Effects of the bifurcation geometry on the flow behaviors of Newtonian and non-Newtonian fluids are numerically investigated. Numerical analyses are focused on the flow patterns in the branch tubes of which angles are 30°, 60° and 90° and on the diameter ratios for Newtonian and non-Newtonian fluids. Variations of the axial velocity and pressure drop along the bifurcated tubes for various flow parameters are presented for Newtonian and non-Newtonian fluids.

Effect of carotid artery geometry on the magnitude and distribution of wall shear stress gradients

Recent information indicates that large, sustained wall shear stress gradients are a dominant hemodynamic parameter associated with the location and severity of atherosclerosis and myointimal hyperplasia. This study computes the spatial values of wall shear stresses and their gradients for three carotid artery bifurcation geometries. A computational fluid dynamics program was used to solve the transient two-dimensional partial differential equations that describe fluid flow. Blood was treated as both a Newtonian and a non-Newtonian incompressible fluid. Solutions for the velocities, wall shear stresses, and wall shear-stress gradients were obtained for three carotid bifurcation geometries: a normal carotid bifurcation (similar to a primarily reconstructed carotid endarterectomy), a patch-reconstructed carotid endarterectomy, and a gradually tapered, low-angle carotid bifurcation (no carotid bulb). Computed velocity profiles closely match published experimental ones. Disturbed flow velocities are largest in the bulb segment of the normal carotid bifurcation. Peak and minimum wall shear stresses and peak shear stress gradients occurred in the lateral internal carotid artery wall. These were binodal in the normal or primarily reconstructed carotid artery, localized at the distal end of the patch-reconstructed carotid bifurcation, and minimal in the smooth, tapered carotid bifurcation. Wall shear stresses and their gradients were slightly higher for non-Newtonian than Newtonian fluids in the normal carotid artery but were similar in the other two geometric configurations. These results indicate that flow disturbances in general and wall shear stress gradients in particular are markedly reduced in carotid artery bifurcations that are smooth and gradually tapered and do not have a bulb. Abrupt geometric wall changes such as those occurring in the normal carotid bulb and at the distal end of a patch-reconstruction after carotid endarterectomy are harbingers of disturbed flow and high wall shear stress gradients. These results suggest that carotid endarterectomy reconstruction geometry characterized by a gradually tapered internal carotid artery may minimize the hemodynamically induced component of early myointimal hyperplasia and thrombosis and late atherosclerotic restenosis.

Computer Simulation of the Flow Field and Particle Deposition by Diffusion in a 3-D Human Airway Bifurcation

ABSTRACT Air flow and ultrafine particle diffusion patterns within an airway bifurcation are investigated by numerically solving the corresponding full Navier-Stokes equations in a three-dimensional curvilinear coordinate system using PHOENICS flow-simulation software. Weibel's human lung morphology, airway generation I = O, was applied in the computer simulation. Computational parameters such as grid sizes, boundary condition treatments, iteration numbers, and convergence criteria have been verified by experimental data measured within the same (mathematically specified) bifurcation geometry. Velocity patterns generated by computer simulation show excellent agreement with the experimental results. Detailed velocity and particle concentration distributions are discussed. Results show that both the inlet and outlet flow boundary conditions have significant effects on the flow and concentration distribution patterns within the bifurcation. The scales of secondary flow within the daughter branches are shown ...

Characteristics of inertial deposition in a double bifurcation

A direct numerical simulation of air flow and particle motion is conducted for doubly bifurcated models in order to see the effect of the velocity profile distorted by the previous bifurcation on particle deposition, because particle deposition in a bifurcated airway is very sensitive to the velocity profile at the inlet, not the magnitude. Flow fields are solved using the FIDAP, an FEM code, and particle trajectories are obtained by a Lagrangean integration. Characteristics of air flow and particle motion in double bifurcations are quite different from what can be imagined based on results for single bifurcation models. The distorted velocity profile can reduce deposition efficiency in the second generation by about 50% when compared with the single bifurcation for the same Stokes number. The bifurcation geometry is also important for particle deposition, and the out-of-plane rotated geometry gives about 40% higher deposition than the in-plane bifurcations.

Air Flow and Particle Deposition Patterns in Bronchial Airway Bifurcations: The Effect of Different CFD Models and Bifurcation Geometries

ABSTRACT The simulation of the experimentally observed inhomogeneity of particle deposition within human airway bifurcations requires the application of numerical methods for the solution of the equations governing the air flow and the motion of particles entrained in the airstream. In this paper, the effects of different computational fluid dynamics (CFD) models and airway bifurcation geometries on the resulting air flow fields and related particle deposition patterns are discussed. First, two different numerical approaches for the solution of the Navier–Stokes equations are compared with each other. In our earlier model (Model I), the three-dimensional air velocity field is calculated with a finite difference code, while the FIRE® finite volume CFD program package is employed in our more recent approach (Model II). The particle deposition parts are similar for both CFD models: trajectories of aerosol particles are simulated under the action of inertial impaction, gravitational settling, Brownian motion,...

Vascular network changes in the retina with age and hypertension

To compare retinal arterial bifurcation geometry in normotensive and hypertensive subjects. A retrospective observational study. Fluorescein angiograms of normotensive (n = 13) and hypertensive (n = 12) subjects aged 30-80 years with uni-ocular retinal pathology were compared. Quantification of diameters of the parent, larger daughter and smaller daughter vessels (d0, d1 and d2, respectively) and of bifurcation angles (the angle between the two daughter arterioles, omega) of arteriolar bifurcations was performed from digitized retinal angiograms of the uninvolved eye. The relative diameters of parent and daughter vessels at bifurcations were summarized by junction exponents (x) such that d1x + d2x = d0x. Junction exponents were similar for normotensives and hypertensives (means +/- SEM, 2.65 +/- 0.18 and 2.48 +/- 0.17), but analysis of covariance showed a parallel decrease in x in the two groups with age. A positive association was found between x and arteriolar microvascular density. Bifurcation angles were more acute in hypertensives (74 +/- 3 degrees) than in normotensives (84 +/- 3 degrees) and declined with increasing age in both groups. The present findings indicate that ageing and possibly hypertension are associated with disadvantageous branching geometry in the human retinal vasculature, implying increased power costs of blood transport, uneven distribution of shear forces throughout the vascular tree and microvascular rarefaction. The present findings may have important implications for our understanding of the pathogenesis of vascular disease in ageing and hypertension and offer the prospect of a novel sensitive diagnostic approach to the cardiovascular system.

Pressure-induced mechanical stress in the carotid artery bifurcation: A possible correlation to atherosclerosis

A possible correlation between regions of high intramural wall stress and the development of atherosclerotic lesions in the carotid artery bifurcation is investigated. The bifurcation geometry is determined through in vivo studies, as well as the analysis of cadaver specimens. Having compiled accurate geometric data, two representative finite element models were created in order to determine the areas of localized stress concentrations that occur in the bifurcation. The artery is assumed isotropic and is mechanically loaded with an incremental pressure of 40 mmHg. A highly localized stress concentration of approximately 9 to 14 times the proximal circumferential wall stress occurs at the point of bifurcation. A lower stress concentration of approximately 3 to 4 times the proximal cirumferential stress occurs over a large area of the sinus bulb. Acknowledging that these two regions of the carotid bifurcation are highly susceptible to atherosclerotic lesions, it appears possible that a correlation between wall stress and atherosclerosis may exist.

Physiologically realistic models of bronchial airway bifurcations

Results of numerical flow field and aerosol deposition calculations in bronchial bifurcations are very sensitive to variations in physical and geometric boundary conditions. In general theoretical models are based on relatively crude geometric approximations due to mathematical and numerical difficulties. Here we define a physiologically realistic bifurcation (PRB) geometry for experimental and theoretical three-dimensional fluid dynamics and particle deposition studies in branching airways. The most significant differences to previous idealized bifurcation models are the reduced skewness of the inspiratory flow, smaller secondary velocity components, and regions of reverse flow in the vicinity of the carine during inspiratory as well as expiratory phases.

G53 - Hypertension and age are associated with disordered retinal arterial bifurcation geometry

G53 - Hypertension and age are associated with disordered retinal arterial bifurcation geometry

10 Hypertension is associated with disordered retinal arterial bifurcation geometry

The Peart-Rose Clinic, St Mary's Hospital and Imperial College of Science, Technology and Medicine, London, UK *Retinal Unit, Western Ophthalmic Hospital, London, UK

Measurement of the geometric parameters of the aortic bifurcation from magnetic resonance images.

This paper presents a method for measuring arterial geometry in vivo using MRI. The approach was validated using MR images of three perfused compliant casts of human aortic bifurcations whose geometry was known. Preliminary human studies demonstrated the reproducibility of the technique. The approach was applied to 20 normal individuals to study the effects of age, race, and gender on the geometry of the aortic bifurcation. The results show that older people tend to have a smaller bifurcation angle, lower planarity, and larger angular asymmetry than younger people. Asians have larger bifurcation angles than whites. The bifurcation of males is more asymmetric than that of females. These results may have implications regarding the heritability of arterial geometry, the similarities of cardiovascular risk within families, and differences in risk among groups.

MR imaging of flow through tortuous vessels: a numerical simulation.

A novel computer simulation technique is presented that allows the calculation of images from Magnetic Resonance Angiography (MRA) studies of blood flow in realistic curving and branching two-dimensional vessel geometries. Fluid dynamic calculations provide flow streamlines through curved or branching vessels. MR simulations generate images for specific MR pulse sequence parameters. Simulations of steady flow in carotid bifurcation and carotid siphon geometries as imaged by a standard, flow-compensated, spoiled gradient echo sequence illustrate the major features seen in clinical time of flight MRA studies. The simulations provide insight into a number of artifacts encountered in MRA such as displacement artifacts, signal pile-up, truncation artifacts, and intravoxel phase dispersion.

Particle deposition in airway bifurcations–II. Expiratory flow

In the present analysis, local inhomogeneities of particle deposition are examined in a bifurcation geometry under realistic expiratory flow conditions, considering the simultaneous effects of inertial impaction, gravitational settling, Brownian motion and interception. The airflow field within the bifurcation during expiration is obtained by solving the Navier-Stokes equations on a three-dimensional computer mesh with a finite-difference technique. Knowledge of the velocity field allows us to simulate the trajectories of aerosol particles entrained in the airstream with Monte Carlo methods. The spatial deposition pattern within the bifurcation is then determined by the intersection of particle trajectories with the surrounding wall surfaces. The effects of particle size, flow rate, inlet flow profile, and bifurcation geometry on the spatial deposition pattern are investigated. In most cases, hot spots are found downstream of the central bifurcation zone. Model predictions are compared with the available experimental data and with other theoretical results.

Arteriolar Bifurcation Angles Vary with Position and When Flow Is Changed

Flow distribution at microvascular bifurcations is influenced by the geometry of the bifurcation region, an area which also is altered pathologically. Bifurcation geometry was measured by in vivo microscopy of the cremaster muscle of anesthetized (Nembutal, 70 mg/kg) golden hamsters ( N = 40), at rest and during maximal dilation (10 -4 M adenosine). The sequential branches had progressively smaller angles of bifurcation at rest: (first position) 118 ± 5°; (second) 89 ± 6°; (third) 78 ± 5°; (last) 58 ± 4°. Between flow conditions, the angle at any bifurcation changed by up to ± 50°, and the angle change was related to position. For the first position, the angles that decreased vs those that increased were significantly different at rest (130 ± 6° vs 109 ± 7°), but not during maximal dilation (119 ± 6° vs 118 ±; 7°). Conversely, at the last bifurcation, the resting angles were not different (58 ± 5° vs 56 ± 7°), but became significantly different during maximal dilation (48 ± 6° vs 68 ± 6°). The axial distance to the first branch ranged between 57 and 857 μm; the angle at the first position was significantly smaller for those first branches that arose further distally along the feed. Further, angles that decreased (vs those that increased) were from significantly longer transverse arterioles (total length: 1820 ± 77 μm vs 1560 ± 61 μm). Resting tone was related to the angle as the smaller angles at the first position, but not at the last position, were more constricted in diameter. Tone was differently related to angle change as the bifurcations that decreased (vs those that increased) in angle were significantly more constricted at the last position (branch diameter rest/maximal: 0.57 ± 0.05 vs 0.81 ± 0.08) but not at the first position (0.66 ± 0.09 vs 0.64 ± 0.05). Thus, we show that the angle of bifurcation varies systematically for sequential branches arising along a single transverse arteriole and that the angles change with flow. This systematic organization for the geometric shape of sequential bifurcation regions may participate in the regulation of flow distribution within this group of arterioles.

Particle deposition in airway bifurcations—I. Inspiratory flow

Bronchial airway bifurcation geometries were constructed in a three-dimensional computer mesh. Air flow fields within these bifurcations were then computed by solving the three-dimensional Navier-Stokes equation with a finite difference method. Trajectories of aerosol particles under the simultaneous action of inertial impaction, gravitational settling, Brownian motion and interception were simulated by solving the particles' equations of motion, using Monte Carlo techniques. This model allowed us to examine spatial deposition patterns, such as hot spots at carinal ridges, within airway bifurcations of the human tracheobronchial tree for inspiratory flow conditions.

Taper: An important feature of y-bifurcations in porcine renal arteries and human cerebral arteries

The geometry of arterial bifurcations has been shown to alter fluid flow and the propagation of both pressure and flow waves. Here we provide a more complete description of the renal artery bifurcation geometry and show that the geometry of the bifurcation is more complex than was believed previously. The objective of this study was to quantify changes in cross-sectional luminal area in systemic arterial bifurcations using the method developed by Macfarlane [Ph.D. thesis, University of Western Ontario, Ontario (1985)] to study the geometry of human cerebral bifurcations. Porcine renal arterial bifurcations from seven young (6–14 weeks) and six old (>52 weeks) animals were pressue-fixed (P = 140 mmHg) for 3 h with 10% formalin. Bifurcations were embedded in a block of frozen latex paint. Serial sections were cut at 20 μm (±0.01 μm) using a sledge microtome while the block face was scanned with a video camera and the images were stored on a videotape. The luminal area was measured digitally upon playback. Bifurcations from the two age groups changed in cross-sectional area not only at the flow divider but also along the socalled straight regions. Proximal linear increases in cross-sectional area were observed proximal to the apex of the bifurcation in both young and old vessels, while linear luminal area decreases were measured in the daughter branches of both young and old porcine renals. Taper was defined as the change in luminal area per unit length of parent and daughter branches, respectively. All tapers were significantly different from zero and were used to compare luminal area changes in young and old renal arteries to human cerebral bifurcations. All vessels showed the same trend: negative taper, or expansion in luminal area, was present in the parent branch proximal to the apex of the flow divider while positive taper was present in the daughter branches. The magnitude of the taper present in both the parent and daughter branches from the two age groups of porcine renals and human cerebral bifurcations were not significantly different (P>0.05). The area ratio, defined as the ratio of the summed luminal area of the daughter branches to that of the parent branch, was not significantly different in the young and the old porcine vessels as well as from the optimum value (1.2). Taper provides a better representation of the changes in luminal cross-sectional area present at bifurcations since area ratios do not take continuous luminal area changes into account and are very dependent on the location of the area measurement. These large luminal area changes, which have been overlooked previously, have significant implications for systemic flow patterns as well as for the propagation of flow and pressure waves.