5-10_Antonova_et al No. 3-4-27_2012

Series on Biomechanics, Vol.27, No. 3-4 (2012), 5-10

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Numerical analysis of blood flow and common carotid artery hemodynamics in the carotid artery bifurcation with stenosis

N. Antonova a, P. Tosheva a, I.Velcheva b

a Department of Biomechanics, Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia Acad.

G. Bonchev str.,bl. 4, Bulgaria, [email protected] b Department of Neurology, University Hospital of Neurology and Psychiatry “St. Naum”, Medical

University. Sofia, Bulgaria, [email protected]

Abstract

Different methods for evaluation of hemodynamics and blood flow and details of numerical simulations in the carotid artery bifucracion with stenosis are overviewed in the present study. Results for blood flow in the carotid artery bifurcation on the basis of numerical simulation of Navier-Stokes equations are presented. The examination of the hemodynamic profile in healthy subjects and patients in parallel with numerical analysis of blood flow and common carotid artery hemodynamics could have a prognostic value for development of carotid atherosclerosis. Keywords: 3D blood flow numerical analysis, carotid bifurcation, stenosis, wall shear stress, whole blood viscosity 1. Introduction

An area of special interest is the carotid artery circulation, where stenoses and other lesions can cause

cerebral disturbances. Possible relation between the carotid pathological lesions and the carotid blood flow give magnetic resonance imaging (MRI), computed tomography (CT) and Doppler ultrasound techniques, developed to measure velocity profiles and vessel morphology with high spatial and temporal resolution. However, complete description of the flow in the human vascular system is difficult because of the complex geometry of the carotid artery bifurcation and the unsteady flow. The use of imaging methods with mapping of wall shear stress distribution (WSS) in the carotid arteries in parallel with numerical simulation could help for detection of the vessel sites where atherosclerotic plaques in the separate individuals would develop.

The WSS represents the frictional force that acts tangentially to the endothelial surface. It is accepted that the chronic exposure of the endothelial cells to high shear stress is accepted to be atheroprotective, while its lower values are associated with thickening of the vessel wall and development of atherosclerotic plaques. In these cases the vascular endothelial cells are exposed to blood flow – induced shear stresses, which cause increase of their membrane fluidity and permeability and activation of the membrane-associated signal proteins – mechanochemical transduction [1,2]. In laminar blood flow, where the fluid velocity profile is parabolic, WSS reflects the relationship of the blood flow velocity, the blood viscosity and the vessel radius. Significant changes in WSS occur in vivo due to different velocities at the sites of curvatures and bifurcations. The pulsatile blood flow, which varies with the cardiac cycle, also influences WSS, which assumes oscillatory pattern [3].

The application of medical image reconstruction for modeling vessel to use in Computational Fluid Dynamic (CFD) has been of rapid development in recent decades. The typical process for performing numerical simulation of blood flow is based on medical imaging, image segmentation, 3D model reconstruction, grid generation and analysis of blood flow solving the Navier-Stokes equations. With the development of modern imaging technology, MRI, CT, etc., it is now possible to quantify arterial blood flow in subject-specific physiologic models and to evaluate the hemodynamics and WSS distribution [1, 2]. With

Antonova et al./ Numerical analysis of 3D blood flow and common carotid artery hemodynamics in the carotid artery bifurcation with stenosis

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the use of CFD simulations and MRI, the ability to evaluate complex relationship between hemodynamics and the predictions of blood vessel damage may be possible.

The study aims to overview different methods for evaluation of hemodynamics in the carotid artery bifurcation in parallel with numerical analysis of blood flow based on Navier-Stokes equations.

2. Methods 2.1. Common carotid artery hemodynamic factors in patients with cerebral infarctions and WSS

The changes of the common carotid local hemodynamic factors like wall shear stress and tensile forces in 16 patients with chronic unilateral cerebral infarctions (CUCI), 58 patients with the main risk factors (RF) for cerebrovascular disease (CVD) like hypertension and hyperlipidemia and 25 healthy control subjects were investigated by Velcheva et al.[1]. The blood flow velocities (BFV), the internal diameters (D) and the vessel wall intima-media thickness (IMT) in the common carotid arteries (CCA) are recorded with color duplex sonography. Systolic (SBP) and diastolic (DBP) blood pressure are measured and mean blood pressure (MBP) is calculated by the formula of Wiggers. Whole blood viscosity (WBV) at the shear rate of 94,5 s-1 is measured on the day of the Doppler ultrasound examination with a rotational viscometer Contraves LS 30. The ultrasound examination by color duplex scanning of the main neck arteries was performed by using a 5 MHz probe with the Versa plus - Siemens instrument. The vessel diameters of the common carotid artery (CCA) in the systole (Ds) and the diastole (Dd), the IMT of the far vessel wall as the mean of 3 consecutive measurements were determined. The systolic (SBFV), mean (MBFV) and diastolic (DBFV) blood flow velocity were detected 1 to 2 cm proximal to the carotid bulb with sample volume in the center of the vessel at an angle of insonation of 450. In the group with CUCI the velocity parameters on the infraction (IS) and non-infarction (NS) side (NS) are compared. The characteristics of the carotid plaques are estimated.The systolic (Ts) and mean (Tm) circumferential wall tension (Tm) are calculated by the formula according to the Laplace law [5]. Wall shear stress (WSS), the circumferential wall tension (T) and the tensile stress (τ) are calculated too. The SBP, WBV and IMT were significantly increased in the patients with CUCI and RF for CVD in comparison to controls. Lower systolic WSS and τ and higher T were established in the patients with CUCI. The IMT correlated with WSS and τ. The study confirms the complex influence of the changes in WBV and blood pressure for the development of carotid atherosclerosis. The findings in patients with cerebral infarctions indicated a higher degree of the vessel wall damage in these patients [4]. 2.2. Analysis of the axial flow field in stenosed carotid artery bifurcation models-LDA experiments

Laser Doppler anemometer (LDA) experiments are performed to gain quantitative information on the differences between the large-scale flow phenomena in a non-stenosed and a stenosed model of the carotid artery bifurcation [6]. Three-dimensional Plexiglass models of a non-stenosed and a 25% stenosed carotid artery bifurcation are perfused with a Newtonian fluid. The flow conditions approximated physiological flow. A shear layer separated the low-velocity area near the non-divider wall from the high-velocity area near the divider wall in which vortex formation occurred during the deceleration phase of the flow pulse. The instability of this shear layer dictated the flow disturbances. The influences of the mild stenosis, located at the non-divider wall, is mainly limited to the stability of the shear layer. No disturbances were found downstream of the stenosis near the non-divider wall. Using a pulse wave with an increased systolic deceleration time, the velocity distribution showed an extended region with reversed flow, a more pronounced shear layer and increased vortex strength. From these measurements it is obvious that the influence of the presence of a mild stenosis, mainly limited to the stability of the shear layer, can hardly be distinguished from the effects of a variation of the flow pulse. The models of the bifurcation are rigid and the compliance of the arterial tree downstream of the bifurcation is not taken into account.

Numerical simulations by Perktold et al. (1991) [7] show that incornoration of the shear thinning behavior of blood did not alter the flow characteristics significantly. The experimental results of Liepsch et al.[8] however, indicated that the viscoelasticity of the fluid could be of importance for the region of flow reversal.


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2.3. Numerical studies of blood flow in the carotid artery bifurcation with stenosis

Numerical study of stenosed carotid bifurcation models based on wall shear stress distribution is presented by Kelvin et al. [9]. Cardiovascular models based on medical image reconstruction of ten patient-specific carotid bifurcations in terms of their geometries and flow properties are used. The characteristics of stenoses at various section of the anatomical structure are used as indicators for explaining the difference in flow properties such as wall shear stress. The geometry of the carotid vessels is extracted from MRI imaging of six patients. The segmentation process includes thresholding and region growing, followed by 3D anatomical reconstruction to obtain a very coarse solid model. During thresholding, a range of gray scale values are selected such that the region to be selected is of best contrast within this range. After the regions of interest were selected and extracted, the voxels are grouped together to form a 3D geometry. Then the reconstruction of carotid bifurcation anatomy into a Computer Aided Design (CAD) model is performed based on the segmentation information. The fluid is assumed to have a density (ρ) of 1.176 g/cm3, viscosity (η) of 4.0 mPa·s and molar mass of 25 kg/kmol. The flow is assumed to be Newtonian and the vessel walls are rigid. The time period T of one cardiac cycle is 0.92 s. The k-ω turbulence model is applied in the simulation. To ensure the convergence of each time step, the convergence criterion for the relative residual of all dependent variables was set to 1×10− 4. For time discretization, the second order backward Euler transient scheme is used.

Steady and unsteady flow patterns are analysed in rigid models of the carotid artery bifurcation by van Steenhoven et al. [10]. Both measurements and calculations were carried out enabling an experimental validation of the numerical method, based on Galerkin's finite element approximation of the Navier-Stokeas and continuity equation. Blood flow in the carotid artery bifurcation with or without stenoses is simulated using the 3D source code by Antonova, Tosheva et al. [11, 12]. Time dependent boundary conditions are used for modeling the development of the blood flow induced by a pulse wave (pressure wave) in the rigid tube. The fluid motion is modeled by solving numerically the system of the Navier-Stokes equations and the continuity equation. Blood is regarded as incompressible fluid with constant density and conservation of mass gives the incompressibility condition. The blood flow around carotid bifurcation (distribution of axial velocity and strain rate) and in the carotid bifurcation containing two and three asymmetrical stenoses placed on the wall of carotid artery is obtained [12]. The results are given at the time point of the maximal pulse wave velocity and are illustrated by the axial velocity and strain rate. The last one is the important facture in the deposition process on the vessel walls.The flow in the bifurcation is strongly unsteady and its visualisation here is very difficult. The pattern of the velocity and the strain rate are presented in the character time point only. To investigate deeply the influence of the stenoses on the blood flow in the bifurcation and deposition processes around it, the stationary part of the flow has to be studied.

Using patient-specific carotid artery bifurcation data from ultrasound imaging Sousa et al. [13] realized a semi-automatic generation of a structured and conformal hexahedral mesh of a nearly planar carotid bifurcation. The geometry, velocity at the inlet (common carotid artery) and at the oulet (internal carotid artery) obtained from ultrasound measurements are imported into the finite element model software to simulate the flow dynamics. The three-dimensional, unsteady, incompressible Navier-Stokes equations are solved with the assumptions of rigid vessel walls and constant viscosity. A good agreement between ultrasound imaging and computational simulated results is achieved.

One example of grid reconstruction and blood flow simulation for a patient with internal carotid artery aneurysms is presented by Xu Bai-nan et al. [14]. The method accurately duplicates the geometry to provide computer simulations of the blood flow. Initial images are obtained by using CT angiography in DICOM format. The image is processed by using MIMICS software, and the 3D fluid model (blood flow) and 3D solid model (wall) are generated. The subsequent output is exported to the Ansys workbench software to generate the volumetric mesh for further homodynamic study. The fluid model is defined and simulated in CFX software, while the solid model is calculated in ANSYS software. The force data calculated firstly in the CFX software are transferred to ANSYS software, and after receiving the force data, total mesh displacement data are calculated in Ansys software. Then the mesh displacement data are transferred back to CFX software. The results of simulation could be visualized in CFX-post. The wall shear stress and wall total


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pressure are in good agreement with the clinical data. 3. Results 3.1. Comparison of Wall Shear Stress

Individual variation in the anatomy of arteries in human is considerable. The degree of blockage is from 9% to 60% and all the bifurcations exhibit some degree of geometrical non-planarity [10]. It has been indicated by previous studies that wall shear stress promotes luminal thinning and plaque rupture and low WSS regions are more prone to athersclerosis. The growth of lesion will lead to stenosis at the artery wall, and further narrowing down stream of the blood vessel will occur. Therefore, this is one of the key parameters that is used for examination of diseased carotid bifurcations. Topological maps of the predicted maximum wall shear stress at peak pressure for each of the ten case studies are given. In all of the models, the maximum wall shear stress (WSSmax) is shown to have peak values on the inner walls of ICA and ECA near the bifurcation points, and significantly elevated values spiralling around the larger angular branch (either the ICA or ECA) from the inner walls along the superior orientation. The maximum (WSSmax) value appeared at the stenosed section due to vessel tapering.

3.2. Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation.

To analyse the pulsatile flow field and the mechanical stresses in a three-dimensional carotid artery

bifurcation model, computer simulation is applied by Perktold et al. [7]. Numerical results are presented for axial and secondary flow velocity and wall shear stresses with special emphasis on the fluid dynamics in the carotid sinus. Flow and stress patterns in human carotid artery bifurcation models, which differ in the bifurcation angle, are analysed numerically under physiologically relevant flow conditions. The governing Navier-Stokes equations describing pulsatile, three-dimensional flow of an incompressible non-Newtonian fluid are approximated using a pressure correction finite element method. The blood non-Newtonian behaviour is modelled by Casson's relation, based on measured dynamic viscosity at supposed rigid blood vessel wall. The results show that the complex flow in the sinus is affected by the angle variation. The magnitude of reversed flow, the extension of the recirculation zone in the outer sinus region and the duration of flow separation during the pulse cycle as well as the resulting wall shear stress are clearly different in the small angle and in the large angle bifurcation. The haemodynamic phenomena, which are important in atherogenesis, are more pronounced in the large angle bifurcation. To simulate the transition zone flow around carotid bifurcation with and without stenoses the wall turbulence model is used by Perktold et al. [15]. Results for different reduction of arterial lumen are received. Blood flow in symmetric stenosis is studied numerically by Antonova et al. [11]. Simulation of blood flow in vessels with different levels of stenoses and with different flow rates is carried out. The results for the pressure drop and wall shear stresses are obtained. To investigate the effect of the distensible artery wall on the local flow field and to determine the mechanical stresses in the artery wall, a numerical model for the blood flow in the human carotid artery bifurcation has been developed [15]. The wall displacement and stress analysis use geometrically non-linear shell theory where incrementally linearly elastic wall behavior is assumed. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier-Stokes equations for non-Newtonian inelastic fluids. In an iteratively coupled approach the equations of the fluid motion and the transient shell equations are numerically solved using the finite element method.

The results show the occurring characteristics in carotid artery bifurcation flow, such as strongly skewed axial velocity in the carotid sinus with high velocity gradients at the internal divider wall and with flow separation at the outer common-internal carotid wall and at the bifurcation side wall. Flow separation results in locally low oscillating wall shear stress. Further strong secondary motion in the sinus is found. The comparison of the results for a rigid and a distensible wall model demonstrates quantitative influence of the vessel wall motion. With respect to the quantities of main interest, it can be seen, that flow separation and


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recirculation slightly decrease in the sinus and somewhat increase in the bifurcation side region, and the wall shear stress magnitude decreases by 25% in the distensible model. The global structure of the flow and stress patterns remains unchanged. The deformation analysis shows that the tangential displacements are generally lower by one order of magnitude than the normal directed displacements. The maximum deformation is about 16% of the vessel radius and occurs at the side wall region of the intersection of the two branches. The analysis of the maximum principal stresses at the inner vessel surface shows a complicated stress field with locally high gradients and indicates a stress concentration factor of 6.3 in the apex region.

The effect of different plaques of trapezoidal, elliptical and triangular shape, imposing 30% reduction of arterial lumen on blood flow through the carotid artery leading to plaque growth and rupture are analysed [16]. A carotid artery model based on statistical analysis called tuning fork model is constructed. Comparison of the results of various CFD simulations show that trapezoidal shape has greater effect on blood flow producing highest flow velocities and wall shear stresses, and creates lowest wall shear stress region downstream of the plaque which may increase the fatty deposits in that area.

In 3D transient analysis it is observed that variation of wall shear stress followed velocity pulse variation and maximum WSS corresponded to maximum velocity. So a steady analysis was performed at maximum velocity of pulse on fine meshes to save computational time. Previous studies show that one of the main factors involved in plaque buildup is low wall shear stress and on the other hand plaque rupture can be due to high shear stress as it causes high flow changes in the vessel. The maximum value of wall shear stress is found on trapezoidal plaque while maximum average wall shear stress was found on elliptical plaque because it causes a continuous change in velocity across its surface. So plaques similar in shape to the trapezoidal plaque may result in more downstream fatty deposit on artery wall.

3.3. Numerical analysis of flow through a severely stenotic carotid artery bifurcation

A model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined by Stround et al. [17]. The work modeled the flow through the severely stenotic ~up to 70% occluded carotid bifurcation as the flow through a rigid-walled vessel and the blood is assumed to have a constant dynamic viscosity of 3.5 mPa.s and mass density 1060 kg/m3.The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady, pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed. Because of the complexity of the geometry involved, only a two-dimensional model has been examined. This model is unable to capture all secondary flow effects in the vessel, but should give a good indication of the flow patterns and shear stresses, which can then be compared with the available in vivo data and with experimental results. The two dimensional model is based on one coronal plane of the three dimensional specimen. Even a mild stenosis has been observed to considerably stiffen artery walls.

4. Conclusion

Different models of the carotid bifurcation were examined. The results of computational simulations

may supplement MRI, CT, Doppler and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. The use of imaging investigation with mapping of wall shear stress distribution (WSS) in the carotid arteries in parallel with numerical simulation could help for detection of the vessel sites where atherosclerotic plaques in the separate individuals would develop. The results from the changes in the hemodynamic profile could also prompt the therapeutic behaviour in the examined patients. Based on MRI, image segmentation, geometry reconstruction and mesh generation could be done. The case studies are based on different anatomies presented by the left, right or common carotid vessel, various degrees of geometrical non-planarity, and variation in severity of stenosis in carotid arteries for a group of


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patients. The physiological geometry can be imported into a CFD solver. As such, this technique can be applied non-invasively at arterial sites where vascular anatomy typically exhibits substantial inter-individual variability. The results play an important role in the formation, growth, rupture and prognosis of damage of the vessel wall and may be a practical tool for planning treatment and follow-up of patients after neurosurgical or endovascular interventions with 3D angiography. The results present the potential of using medical imaging and numerical simulation to provide existing clinical prerequisites for diagnosis and therapeutic treatment. Acknowledgements

The Ministry of Education, Youth and Science of Bulgaria supported the study - funded by the Operational Programme "Human Resources Development" within the Project № BG051PO001-3.3-05/0001 regimen «Science-Business" under Grant No. ДО-803/2012 is gratefully acknowledged.

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5-10_Antonova_et al No. 3-4-27_2012