Elsevier

Journal of Biomechanics

Volume 64, 7 November 2017, Pages 153-163
Journal of Biomechanics

Analysis of non-Newtonian effects within an aorta-iliac bifurcation region

https://doi.org/10.1016/j.jbiomech.2017.09.042Get rights and content

Abstract

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.

Introduction

The abdominal aorta is the largest artery in the abdominal cavity. As part of the aorta, it is a direct continuation of the descending aorta (of the thorax). Common iliac arteries (right to left) diverge as they descend and divide at the level of sacro-iliac joint into external and internal iliac arteries (Standring, 2008).

The anatomical description of aortic-common iliac region is well known. The geometry of the arteries at or near arterial bifurcation influences the blood flow field, which is an important factor affecting artherogenesis. Thus, an individual’s unique arterial geometry might influence that person’s risk of arterial diseases. The anatomy of the aorta and its relationship to the vertebra would provide useful information to the surgeon for the anterior lumbosacral approach (Shah et al., 1978). The purpose of the study carried out by Bargeron et al. (1986) is to call attention to the variability in flow-divider offset and angular asymmetry and to present their distributions and those of the branch angle among human aortic bifurcations. The authors carried out a retrospective study to objectively determine the distributions of angles and offsets within a collection of 70 aortic bifurcations. They created computer routines that calculated these quantities using as input the wall contours obtained from frontal-plane radiographs of these arterial segments.

The aim of a recent study presented by Deswal et al. (2014) was to determine the position of aortic bifurcation, diameter of distal aorta in relation to the lumbar vertebra, length of common iliac arteries, diameter of iliac at bifurcation and aortic bifurcation angle. The study was done on 25 cadavers (16 males, 9 females) used for the dissection by 1st year MBBS (Bachelor of Medicine and Bachelor of Surgery) students. The dissections were performed by anterior approach to the lumbar vertebra. The position of the aortic bifurcation and aortic bifurcation angle were measured in relation to the lumbar vertebra. The remaining parameters were measured with the help of a digital vernier caliper.

Hemodynamic factors are thought to be responsible for the localization of vascular disease in areas of complex flow in the coronary, carotid, abdominal, and femoral arteries. These complex flow regions often occur due to branching, bifurcations, and curvature of the arteries. Zarins et al. (1983) noted that in the carotid artery, atherosclerotic lesions localize along the outer wall of the carotid sinus region where wall shear stress is low. Conversely, the inner wall of the carotid sinus, an area of rapid, laminar and axial flow, and high wall shear stress, was observed to be devoid of plaque.

In recent years, computational techniques have been used increasingly by researchers seeking to understand vascular hemodynamics. These methods can augment the data provided by in vitro and in vivo methods by enabling a complete characterization of hemodynamic conditions under precisely controlled conditions. Application of these methods to flow in the carotid bifurcation and bypass grafts has provided significant information on vascular hemodynamics. Perktold et al. (1991) used a finite element method to simulate the pulsatile flow of a Newtonian fluid in a model of a carotid artery bifurcation using a rigid wall approximation. Detailed results on the velocity, pressure, and wall shear stress were presented. Numerical methods are well suited for an investigation of phenomena difficult to describe using in vitro techniques including wall compliance, mass transport, particle residence time, and geometric variations. In an investigation of the effect of wall compliance on pulsatile flow in the carotid artery bifurcation, Perktold and Rappitsch (1995) describe a weakly coupled fluid–structure interaction finite element method for solving blood flow and vessel mechanics.

In contrast to the relatively large number of studies on pulsatile flow in models of the carotid bifurcation and end-to-side anastomosis, there have been few numerical studies of flow in the abdominal aorta. It is important to understand fluid behavior in this zone in order to catch features like Low-Density Lipoprotein (LDL) deposition, that is strongly related with shear stresses at the walls (Nematollahi et al., 2012). Taylor et al. (1995) describe the flow in an abdominal aorta model under simulated resting and exercise steady flow conditions. It was noted that a region of flow recirculation and low wall shear stress develops along the posterior wall of the infrarenal abdominal aorta under simulated resting conditions and disappears under simulated moderate and vigorous exercise conditions. Successively, a computational method was used to quantitatively characterize the hemodynamic conditions under simulated resting pulsatile flow conditions in an idealized model of an abdominal aorta (Taylor et al., 1998). This article details the mean wall shear stress and shear stress oscillations in the abdominal aorta. Long et al. (2000) describe a novel combined experimental and computational approach for studying flow in the distal human aorta and common iliac arteries in which Magnetic Resonance Imaging (MRI) is used to obtain measurements of arterial geometry and blood velocity, and thus provide the anatomical and hemodynamic input conditions necessary for detailed Computational Fluid Dynamic (CFD) simulations. Results confirm that in vivo flow patterns may differ substantially from those predicted by conventional fluid dynamic models. The combined imaging/computational approach allows the derivation of WSS (Wall Shear Stresses) distributions during different phases of the cardiac cycle, which cannot be measured directly in the human vascular system. A three-dimensional unsteady model of small arteries reconstructed by means of ultrasonic images was presented by Abraham et al. (2008). Images were obtained before and after plaque removing process. From their results, it has been possible to conclude that plaque removal causes an increase in terms of blood flow rate. An analysis of fluid flow and mass transfer in the aorta-iliac bifurcation was performed by Khakpour and Vafai (2008). They analyze various geometrical configurations that depend on the gender, showing that it affects both WSS and LDL deposition. A numerical simulation of oscillatory flow through the abdominal aortic bifurcation was carried out by Gohil et al. (2011). The paper reports a detailed comparison of simulations performed with a finite volume and a finite element method. Waveform effects on fluid-dynamics parameters have been discussed by Naughton et al. (2014). They developed a model for an aneurism geometry obtained from medical images. A patient-based waveform is employed, while various cardiac cycles were analyzed by modifying the aforementioned waveform. They concluded that results were in good agreement among each other, even if input waveform were manipulated. The impact of plaque on the artery wall compliance was numerically analyzed by Vallez et al. (2015), reporting that low reductions in plaque thickness cause large changes in terms of compliance. Pressure drop and flow rate through popliteal artery, that is susceptible to plaque lesions, have been analyzed by Plourde et al. (2015). They also compared their results with experimental results obtained before and after treatment, showing a good agreement in terms of pressure. Numerical simulations in an artery before and after removing the plaque were performed by Plourde et al. (2016), showing that atherectomy increases flow through the stenotic zone, with a decrease in terms of pressure drop. From all the mentioned papers, it can be concluded that geometrical features have a primary role in modeling fluid-dynamic behavior of blood through, thus it is very important to customize the studies depending on the specific case. For example, it can be gender-related geometrical features like the ones reported by Shah et al. (1978) for the aorta-iliac bifurcation. Further, employing an idealized model instead of a computationally-reconstructed model with techniques like Computed Tomography (CT) is very convenient in terms of costs.

In general the blood can act as a non-Newtonian fluid (Ross Ethier and Simmons, 2007). However, many studies have argued that for large arteries (Cho and Kensey, 1991, Lou and Yang, 1993, Perktold et al., 1999, Johnston et al., 2004, Mandal, 2005, Johnston et al., 2006, Ross Ethier and Simmons, 2007, Yilmaz and Gundogdu, 2008), and in some cases for medium arteries (Ross Ethier and Simmons, 2007), the blood flow can be considered to be Newtonian, also for mass transfer problems (Iasiello et al., 2016). Several studies have discussed the influence of non-Newtonian characteristics on the blood flow. Gijsen et al. (1999a) analyzed non-Newtonian properties in large arteries in the carotid bifurcation. They carried out Laser Doppler Anemometry (LDA) measurements by using a blood analog fluid that includes non-Newtonian properties of the blood. Such measurements were compared with numerical simulations performed on Newtonian blood flow model and on Carreau-Yasuda blood flow model with coefficients obtained from experiments. They found generally good agreements with experiments for both Newtonian and non-Newtonian cases. For the latter, more flattened axial velocity profiles, higher velocity gradients at the non-divider wall and lower velocity gradients at the divider wall, were found. A similar analysis of non-Newtonian effects in a 90° curved tube was performed by Gijsen et al. (1999b). Johnston et al. (2004) defined an index that quantifies the importance of non-Newtonian effects for both steady state (Johnston et al., 2004) and transient state (Johnston et al., 2006). This index has been extended on stenosed arteries by Razavi et al. (2011), who have also stated that Carreau and Carreau-Yasuda are the two models that provide closer results to a Newtonian model. Ross Ethier and Simmons, 2007 have reported some typical hemodynamic values for a 70 kg human. They had concluded that, for the typical shear rate values, blood can be treated as Newtonian for most of the large arteries. Newtonian assumption can incur some inaccuracy, for example when hematocrit level is increasing (Yilmaz and Gundogdu, 2008, Mandal, 2005), or when Wall Shear Stresses (WSS) becomes lower (Cho and Kensey, 1991, Lou and Yang, 1993, Mandal, 2005, Iasiello et al., 2016). However, it is important to understand these aspects, since employing a Newtonian fluid model is a very useful simplification in common practice.

In the present study, 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 reference to the values reported in Shah et al. (1978), for both male and female genders. Governing equations with the appropriate boundary conditions are solved with the commercial finite-element code COMSOL Multiphysics. Different non-Newtonian fluid models are used and detailed comparisons are presented for the aorta-iliac bifurcation. Results are presented in terms of velocity profiles in the bifurcation zone, WSS for different sides of the bifurcation both for a male and female geometries. It is established that in general the Newtonian assumption is mostly valid, especially at higher velocities.

Section snippets

Mathematical model, numerical analysis and experimental validation

A sketch of the three-dimensional aorta-iliac geometry is depicted in Fig. 1. The aorta-iliac geometry is reconstructed with reference to the values reported in Shah et al. (1978), given in Table 1. The values herein reported are taken as averaged over 14 males and 12 females aorta-iliac bifurcations. It is mentioned that the definition of the right and left iliac, and all the variables related, depends on the reference system, and that the results reported in the following are independent of

Results and discussion

Simulations are performed also for different inlet velocities, i. e. between 0.1 and 0.4 m/s. These values are in the typical velocity order of magnitude referred to the aorta. In the present study, Reynolds number vary from 494 to 2270, with which the laminar flow assumption is assumed to be valid since it is less than 2300. In order to investigate the flow change of direction due to the bifurcation, various velocity profiles and fields are reported in Fig. 4. In Fig. 4(a) and (b), the change

Conclusions

A comprehensive investigation of non-Newtonian effects on the blood fluid dynamic behavior in an aorta-iliac bifurcation is presented. Governing equations with the appropriate boundary conditions are solved numerically employing a 3D formulation. Different rheological models are used for the blood flow through the lumen.

Velocity profiles and fields are reported along the flow direction; it is shown that the profile changes when approaching the bifurcation and it tends to move in a preferential

Conflict of interest

There is no conflict of interest. This manuscript has not been submitted to anywhere else.

References (37)

Cited by (33)

  • Computational analysis of one-dimensional models for simulation of blood flow in vascular networks

    2022, Journal of Computational Science
    Citation Excerpt :

    According to these models, the viscosity gradually decreases/increases with the shear rate increase/decrease, reaching two different plateau values, — this effect is demonstrated in many experiments on blood rheology [33–35]. The following models of such type are considered in the literature: Carreau model [24,26–28,32,33,36–42], Carreau–Yasuda model [22,24,26–28,30,32,33,36–44], Cross model [26–28,33,36,38,45,46], simplified Cross model [33,47], modified Cross model [24,26,33,38,47], Powell–Eyring model [33,38,47–49], modified Powell–Eyring model [33,38,47] and Yeleswarapu model [50–53]. Some generalized Newtonian models are dependent on the value of hematocrit.

  • Comparison of inviscid and viscid one-dimensional models of blood flow in arteries

    2022, Applied Mathematics and Computation
    Citation Excerpt :

    As the main result of their investigation, it is stated, that for this problem the Newtonian assumption can be made without any particular loss in terms of numerical accuracy. In [33], the non-Newtonian effects on low-density lipoprotein transport across the artery are analyzed. For the aorta-iliac bifurcation flow, it is demonstrated that the Newtonian assumption is valid for mass transport at low Reynolds numbers.

  • Effects of Brownian motions and thermophoresis diffusions on the hematocrit and LDL concentration/diameter of pulsatile non-Newtonian blood in abdominal aortic aneurysm

    2021, Journal of Non-Newtonian Fluid Mechanics
    Citation Excerpt :

    In this regard, there is a controversy among scientists to model blood flow as Newtonian or non-Newtonian flow. Certain scientists have suggested that blood acts like Newtonian flow inside larger arteries like aorta while some have assumed pulsatile blood flow as non-Newtonian flow since the wall shear stress of this flow is not negligible [26–30]. Furthermore, a number of studies have applied pulsatile blood in order to investigate the hemodynamic parameters [38–40].

View all citing articles on Scopus
View full text