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The geometry of the arteries at or near arterial bifurcation influences the blood flow field, which is an important factor affecting arteriogenesis. The blood can act sometimes as a non-Newtonian fluid. However, many studies have argued that for large and medium arteries, the blood flow can be considered to be Newtonian. In this work a comprehensive investigation of non-Newtonian effects on the blood fluid dynamic behavior in an aorta-iliac bifurcation is presented. The aorta-iliac geometry is reconstructed with references to the values reported in Shah et al. (1978); the 3D geometrical model consists of three filleted cylinders of different diameters. Governing equations with the appropriate boundary conditions are solved with a finite-element code. Different rheological models are used for the blood flow through the lumen and detailed comparisons are presented for the aorta-iliac bifurcation. Results are presented in terms of the velocity profiles in the bifurcation zone and Wall Shear Stress (WSS) for different sides of the bifurcation both for male and female geometries, showing that the Newtonian fluid assumption can be made without any particular loss in terms of accuracy with respect to the other more complex rheological models., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Understanding the functional performance of vascular tissue is taking a rising importance due to the increasing impact of cardiovascular diseases in developed countries. Currently available medical imaging acquisition techniques, combined with computer modelling allow patient-specific simulations of customized geometries that may help in medical diagnosis and therapeutic treatment. In this work we show methodology to develop patient-specific simulations. Particular features of arteries such as their multilayered structure, as well as the non-linear behaviour of the arterial tissue are considered. A strategy based on the decomposition of the deformation gradient tensor is followed in order to include residual stresses in the real geometry. By means of this technique, it is also possible to model the adaptative growth of the artery neglecting the developing process from the embryo state.

In the present study, a numerical calculation procedure based on a finite volume method was developed to simulate steady flow fields in a model of abdominal aorta with its peripheral branches. The study focused on the steady baseline flow fields and the wall shear stress (WSS) distribution as well as the localization of the reversed flow regions and results were compared to those obtained by other investigators. In the case of resting conditions, the existence of a region of reversed flow of about one to two diameters in size and next to the renal arteries and along the posterior wall as observed by other researchers was confirmed. However, under the exercise conditions this region could be wiped out. The flow reversal along the lateral walls proximal to the bifurcation persisted in both rest and exercise conditions. The WSS distribution and the wall shear stress gradient distribution were obtained. The lowest WSS occurred near the ostia of the renal arteries and the lateral walls of the iliac arteries. And the highest is always at the turn to the branch. The results were generally consistent with those obtained experimentally and numerically by other investigators. It was also shown that the steady flow might be used to depict the averaged behavior of pulsatile flow. The present computer code provides a platform for the future more realistic simulations.

Flow in the aortic arch is characterized primarily by the presence of a strong secondary flow superimposed over the axial flow, skewed axial velocity profiles and diastolic flow reversals. A significant amount of helical flow has also been observed in the descending aorta of humans and in models. In this study a computational model of the abdominal aorta complete with two sets of outflow arteries was adapted for three-dimensional steady flow simulations. The flow through the model was predicted using the Navier-Stokes equations to study the effect that a rotational component of flow has on the general flow dynamics in this vascular segment. The helical velocity profile introduced at the inlet was developed from magnetic resonance velocity mappings taken from a plane transaxial to the aortic arch. Results showed that flow division ratios increased in the first set of branches and decreased in the second set with the addition of rotational flow. Shear stress varied in magnitude with the addition of rotational flow, but the shear stress distribution did not change. No regions of flow separation were observed in the iliac arteries for either case. Helical flow may have a stabilizing effect on the flow patterns in branches in general, as evidenced by the decreased difference in shear stress between the inner and outer walls in the iliac arteries.

The three-dimensional flow through a rigid model of the human abdominal aorta complete with iliac and renal arteries was predicted numerically using the steady-state Navier Stokes equations for an incompressible. Newtonian fluid. The model adapted for our purposes was determined from data obtained from cine-CT images taken of a glass chamber that was constructed based on anatomical averages. The iliac arteries had a bifurcation angle of approximately 35 and a branch-to-trunk area ratio of 1.27. whereas the renal arteries had left and right branch angles of 40 and an area ratio of 0.73. The numerical tool FLOW3D (AEA Industrial Technology, Oxfordshire, UK) utilized body-fitted coordinates and a finite volume discretization procedure. Purely axial velocity profiles were introduced at the entrance of the model for a range of cardiac outputs. The four-branch numerical model developed for this investigation produced flow and shear conditions comparable to those found in other reported works. The total wall shear stress distribution in the iliac and renal arteries followed standard trends. with maximum shear stresses occurring in the apex region and lower shear stresses occurring along the lateral walls. Shear stresses and flow rate ratios in the downstream arteries were more effected by inlet Re than the upstream arteries. These results will be used to compare further simulations which take into effect the rotational component of flow which is present in the aortic arch.

A surgical study (Bergeron et al., 1991, International Angiology 10(3), 182-186) picked out that re-endothelialization of implanted expandable stents, frequently used to reduce the recurrent stenosis rate after balloon angioplasty, was correct and more rapid in femoro-popliteal arteries (quasi-straight vessels) than in iliac arteries (bifurcated vessels). Since it is now well known that local hemodynamics are considered to be an important atherogenic factor, we decided to compare and optimize the shape of the existing equipment, in order to further give some informations to surgeons about the optimal stenting at the site of bifurcation. Therefore, we studied in vitro (1) the influence of the protruding part of a stent on the flow patterns in the branches of an aorto-iliac bifurcation model, and (2) the possibility of reducing or preventing this impact. Qualitative information was obtained from visualizations in the horizontal median plane of the bifurcation model, while Doppler ultrasonic velocimetry provided quantitative data, at different points of the cardiac cycle. Results showed that a standard stent implanted in a daughter branch of the bifurcation may have a considerable influence on flow behaviour when it is sticking out of the daughter branch. A new design of stent, with a bevelled shape, showed a significant reduction of flow disturbance.

The infrarenal abdominal aorta and aortic bifurcation are frequent sites of atherosclerosis. The local hemodynamics are considered to be an atherogenetic factor, and a detailed description of the flow fields in this region of the arterial tree is therefore essential. The aim of this study was to provide quantitative two-dimensional data on the velocity fields in the abdominal aorta, using a realistic flow model of the abdominal aorta and its main branches, under various physiologic flow conditions (i.e. rest and exercise). Velocities in the suprarenal abdominal aorta were antegrade, with very little retrograde and radial velocity components present. In the infrarenal abdominal aorta, velocity profiles were not fully developed, and large-scale retrograde flow was present during part of diastole for the rest condition. For the exercise conditions small-scale retrograde velocities were present during diastole, especially at the distal posterior vessel wall, but not at the distal anterior vessel wall. For the rest and medium exercise conditions, secondary flows were created in the distal abdominal aorta during diastole, most prominent near the posterior wall. Calculated wall shear stress directions revealed the presence of both oscillatory and multidirectional wall shear stresses mainly in parts of the infrarenal abdominal aorta, and were found to correlate well with the published data on the distribution of early atherosclerotic lesions. This quantitative study demonstrates the necessity of carefully modeling both the anatomy and the physiology in order to understand the complex hemodynamics present in the abdominal aorta.

A two-dimensional numerical model was developed to determine the effect of the non-Newtonian behavior of blood on a pulsatile flow at the aortic bifurcation. The blood rheology was described by a weak-form Casson equation. The successive-over-relaxation (SOR) method was used to solve both the vorticity and Poisson equations numerically. It was disclosed that the non-Newtonian property of blood did not drastically change the flow patterns, but caused an appreciable increase in the shear stresses and a slightly higher resistance to both flow separations and the phase shifts between flow layers.

Reflections of pulse waves will occur in arterial bifurcations unless the impedance is matched continuously through changing geometric and elastic properties. A theoretical model is presented which minimizes pulse wave reflection through bifurcations. The model accounts for the observed linear changes in area within the bifurcation, generalizes the theory to asymmetrical bifurcations, characterizes changes in elastic properties from parent to daughter arteries, and assesses the effect of branch angle on the mechanical properties of daughter vessels. In contradistinction to previous models, reflections cannot be minimized without changes in elastic properties through bifurcations. The theoretical model predicts that in bifurcations with area ratios (beta) less than 1.0 Young's moduli of daughter vessels may be less than that in the parent vessel if the Womersley parameter alpha in the parent vessel is less than 5. Larger area ratios in bifurcations are accompanied by greater increases in Young's moduli of branches. For an idealized symmetric aortic bifurcation (alpha = 10) with branching angles theta = 30 degrees (opening angle 60 degrees) Young's modulus of common iliac arteries relative to that of the distal abdominal aorta has an increase of 1.05, 1.68 and 2.25 for area ratio of 0.8, 1.0 and 1.15, respectively. These predictions are consistent with the observed increases in Young's moduli of peripheral vessels.(ABSTRACT TRUNCATED AT 250 WORDS)

We have determined the velocity profiles and wall shear rates along the New Zealand White (NZW) rabbit aortoiliac bifurcation. A pulsatile perfusion apparatus was used to impose physiologic pressure and flow waveforms on nine freshly excised NZW bifurcation segments. Pulsed Doppler velocimetry (PDV) was utilized to construct velocity profiles at five measurement sites: within the infrarenal aorta; immediately distal to the apex of the bifurcation; and, more distally along the iliac arteries. Wall shear rate was derived from a numerical differentiation of the experimental velocity profiles. The results of this study indicate that the average shear rate was lower along the lateral (approximately 40 s-1) vs medial (approximately 240 s-1) wall of the proximal iliac branch. The degree of flow reversal along the proximal lateral walls (20 +/- 2%) exceeded that along the proximal flow divider wall (1 +/- 1%). Flow at the distal iliac measurement sites and within the infrarenal aorta was approximately symmetric. These findings complement our companion in vivo study [Berceli et al., Arteriosclerosis 10, 688-694 (1990)] wherein we determined the rates of low-density lipoprotein (LDL) incorporation and catabolism along this symmetrically bifurcating conduit. Taken together, these studies provide original information regarding the effects of hemodynamics on one presumed atherogenic risk factor, namely, LDL metabolism.

The infrarenal abdominal aorta and aortic bifurcation are frequent sites of atherosclerosis. The local hemodynamics are considered to be atherogenetic factors; a detailed description of these flow fields is, therefore, essential to understand their relationship to atherosclerosis. The aim of this study was, therefore, to provide such detailed information using a flow visualization technique in an anatomically realistic flow model of the abdominal aorta and its main branches in which the complex pulsatile flow waveforms and flow rates were simulated for two physiologic flow conditions (rest and exercise). At rest, the particle path lines in the suprarenal abdominal aorta were straight with no visible signs of flow reversal. Vortices were initiated opposite to the main branches. In the infrarenal aorta, large flow separation zones formed at the posterior aortic wall and at the lateral walls in the aortic bifurcation during systolic deceleration, and flow reversal was present during diastole. Under exercise conditions, the particle path lines were straight, and only slight flow reversal was seen. This study emphasizes, that rather than being a straight tube with forward-moving fluid, the abdominal aorta has to be considered as a complex part of the arterial tree. Distinct local hemodynamic qualities of importance for explaining atherogenesis were pointed out. At rest, the suprarenal abdominal aorta had much less complicated flow characteristics than the infrarenal abdominal aorta where the distal, posterior vessel wall and the lateral walls of the bifurcation were sites of flow patterns thought to be associated with atherosclerosis. During exercise, the infrarenal flow patterns changed dramatically away from the flow patterns associated with the induction of atherosclerosis.

Shear rates measured at sites along the walls of ten casts of human aortic bifurcations are presented to provide an indication of the variability in the shear rate distribution that can occur among individuals. The geometric characteristics and flow parameters for each of the casts are also given. Much of the variability in wall shear distribution seen here results from variations in arterial geometry; variations in flow parameters can widen further the normal range of shear distributions.