Cardiovascular Disease and Computational Fluid Dynamics (CFD) Simulation of Flow in 2D Carotid Bifurcations

Transcription

1 Cardiovascular Disease and Computational Fluid Dynamics (CFD) Simulation of Flow in 2D Carotid Bifurcations INTRODUCTION One of the major health problems in United States is stroke and currently it becomes the third in ranking. Out of 5, new patients recorded, approximately 7 percent of the patients survived. Fortunately, overall cases have been decreased. However, nearly 5 percent of the strokes victims need assistance to manage their daily lives and out of that, 1 percent need full health attention and assistance. Overall economic expenses for stroke cases achieve to $15 billion per year. The increased of mortality and morbidity in this area motivated the researchers to study deeply in preventing this problem. Ischemic stroke is caused by atherosclerotic lesions in the extracranial vessels and it affected about 75 percent of the patients. Subarachnoid hemorrhage and primary intracerebral hemorrhage are other major causes of stroke. Stroke or transient ischemic attack is the symptoms of carotid stenosis. It also can be detected at an asymptomatic stage. The short term action for the patient with atherosclerotic carotid bifurcation stenosis is the prevention of neurological morbidity and mortality. The patients suffered from carotid stenosis are divided in two stages: asymptomatic and symptomatic. Asymptomatic is the stage where the problem detected on the patient during normal physical test or while examine the patient for other disease. While symptomatic is the stage where the problem detected may show the symptom such as transient ischemic attacks or stroke. Several invasive treatments have been performed to reduce the carotid artery problems such as coronary artery by-pass surgery, balloon angioplasty/stenting and laser or rotational ablation of plaques. However, before performing any treatment on the patients, analysis and measurement are required on the problem area. It is unpleasant and difficult to perform analysis and measurement on the human body but by simulating using the computer software, it makes the process less hazard. The geometry of the vessel such as bifurcation angle, carotid sinus size and wall thickness affects the fluid and solid mechanics of the system. Therefore, the difference of geometry between human internal organs is important when attempting to relate biomechanics of blood, vessel and atherosclerosis. A Computational Fluid Dynamics (CFD) approached has been applied to observe the blood flow simulation in the carotid bifurcation. The purposed of this study is to perform flow simulation of a carotid bifurcation without stenosis and stenosis by using commercial CFD code. Furthermore, the results from the analysis need to be analysed by using CFD post- processor. Moreover, the analysis required the understanding of model geometry changing that influence the flow patterns. 1

2 METHODOLOGY The common carotid artery (CCA) is divided into two branches which the internal part is called internal carotid artery (ICA) and the external part is called external carotid artery (ECA). They are shown in Figure 1. The function of ICA is supplying oxygenated blood from the heart to the anterior part of the brain while ECA supplies the oxygenated blood from the heart to the face and neck tissues. The atherosclerotic plaque and stenosis commonly develop above the bifurcation in the bulb of ICA. Figure 1: Schematic shows diameter of a carotid arterial bifurcation. In this study, the comparison of the blood flow between the healthy carotid arterial bifurcation and the carotid arterial bifurcation with stenosis has been performed as refer to the certain parameters. The schematic in Figure 1 shows the diameter of a healthy carotid arterial bifurcation. The diameter of the CCA is 8 mm and increased to 48 mm towards the centerline of curvature. The ICA diameter narrowed from 8.9 mm to 5.6 mm while ECA diameter also narrowed from 5.6 mm to 4.6 mm. The open angle from the centerline towards ICA is 25 degree and open angle from the centerline towards ECA is 3 degree. The inlet flow is from the CCA while there are two outflows, one at the end of ICA and the other one at the end of ECA. ECA CCA origin ICA ICA branch has been narrowed to observe the simulation result with stenosis Figure 2: The stenosis carotid arterial bifurcation 2

3 The carotid arterial bifurcation with stenosis is illustrated using Gambit; it is shown in Figure 2. In this case, the size of the bulb in ICA has been reduced to half of the normal size of the diameter. All the parameters in the carotid arterial bifurcation remain at the actual size, except at the ICA bulb. The reason of doing this is to observe and compare the blood flow performance and pattern in the carotid arterial. The image of common carotid bifurcation with stenosis during angiogram from the stroke patient shown in Figure 3. Figure 3: The image of stenosis carotid bifurcation SIMULATION PARAMETERS i. Blood Flow Simulation. The type of flow is a two dimensional steady blood flow with Reynolds Number (Re) in the range of 2 to 4. The blood density, is known as 16kg/m 3 and viscosity, is known as.36kg/ms. The flow velocity is defined as V and the diameter of the arterial is defined as D (depend on the diameter of the branches). The theoretical calculation for Re at all branches form as VD Re = At CCA, the diameter is.8m, V from the inlet is assumed as.1m/s and the Re is calculated as Re = Re = 236 At ECA branch, when the diameter is.56m, V is assumed as.2m/s and the Re is calculated as 3

4 Re = Re = 33 At ECA branch, when the diameter is.46m, V is assumed as.2m/s and the Re is calculated as Re = Re = 271 At ICA branch, when the diameter is.89m, V is assumed as.15m/s and the Re is calculated as Re = Re = 393 At ICA branch, when the diameter is.56m, V is assumed as.15m/s and the Re is calculated as Re = Re = 247 The calculation of Re comparing the flow in the ICA bulb with stenosis which V is assumed as.1m/s and D is half of the normal diameter which is.445m calculated as Re = Re = 2 Hence, the calculation of the Re shows that Re>>1 which means the flow is dominated by inertia not viscosity. The velocity and diameter of the arterial influence the Re. ii. Physical Model. The physical model shown in Figure1 is measured in millimetres. In Gambit, the model is scaled three times larger compare to the original size. The Carotid Bifurcation contains of three branches which is CCA, ECA and ICA. The inlet begins at CCA, the first outflow toward the end of ECA and the second out flow toward the end of ICA. It is created in the horizontal of X direction. 4

5 iii. Mesh Edge Distribution (Grading). The grid is designed into three types which have the same size and diameter but different density. The reason is to observe and study the flow performance in the different type of mesh. These grids are also applied to the carotid artery with stenosis and the ICA branch has been narrowed at the bulb for this purpose. The basic type of grid is shown in Figure 4. It is designed with grid ratio is 1 and specifying the number of edge divisions by interval count. It is applied to stenosis and without stenosis. WALL1 INLET WALL2 CCA WALL3 ECA WALL4 OUTFLOW1 WALL 8 WALL7 ICA A WALL6 Figure 4(a) WALL5 OUTFLOW1 Figure 4(b) Figure 4: (a) Meshed without stenosis carotid artery in a basic grid and the boundary condition for all the simulation and (b) Meshed stenosis carotid artery. Another two types of edges division is specified by different interval count where the grid ratio of the horizontal edges is 1. The vertical edges are set to double sided or invert grid and different interval count. The flow domain meshing elements and types are Quad/Tri and Map. The stenosis mesh diagrams are also set for simulation purposed and discuss the result in the following section. The benefit of using a double sided grading on the vertical faces is to concentrate elements closer to the wall in order to better resolve the relatively large velocity gradients present in the boundary layer. The quality of the grid in any CFD problem is a major contributor to the quality of the solution [4]. Although fine grids are more accurate, sometimes it is less stable. The grid adaptation can be done by generating a finer grid using the existing grid. At the solver, the grid is coarsened by merging several neighbouring control volumes into one volume. An approximate solution is obtained for the coarser grid that is applied as a starting point to the grid. 5

6 iv. Model Geometry. The model geometry plotted by defining the origin (Figure2) at any convenient central position, co-ordinates x and y, then connect the vertices to form edges. Hence, specifying the region of the flow domain at the beginning of the inlet then follow by other edges to form a close loop region. This is called face. There are three faces divided from this model. The model geometry for all the generated meshes is plotted in the appendix 1. v. Boundary Conditions. Gambit is used to generate grids for a numerical solver such as fluent. Fluent uses the unstructured mesh to simplify the modeling geometry and simulate the mesh to produce the flow performance. Boundary conditions are required at all boundaries around the flow domain. The wall boundary condition is specifies by zero velocity at the wall. FLUENT by default assumes a wall for the types of boundaries, unless the walls have been specified with the specific region. The types of boundary conditions are flow inlet, outlet, wall, repeating boundaries and internal cell zones. In this study the boundary condition is specified as Figure 4(a). In this case FLUENT 5/6 has been chosen for the type of boundaries definition. However these are depend on the solver application. vi. vii. Solution Techniques. The flow equations are solved by using FLUENT domain. It is required to define the flow type, the boundary conditions, fluid properties and other related parameters. The program starts by using 2D program. The FLUENT read the mesh file exported from Gambit and check the grid. This process may produce a grid check error especially when the minimum volume is positive. The scale need to be changed according to the model requirement. In the numerical models solver, the flows remain laminar and isothermal. The material is defined as blood with density 16 kg/m 3 and viscosity.36kg/ms. The inlet velocity zone defined in Gambit is checked to be associated with the inlet velocity type in FLUENT at define boundary condition. The inlet velocity is.1m/s and the velocity specification method is changed to components. The information are provided to the solver such as control solution are set as default under-relaxation values and the discretization schemes (first-order upwind for momentum), then initialized from the inlet. Set plot at residual monitor, then iterate of 5 to observe the iterative solution process. Convergence Criteria. All the iterative/numerical solution procedure may only give a solution which is converged relative to some criteria. The solution may be converged if all discretized transport equations are 6

7 obeyed to a specified tolerance defined by Fluent residuals, the solution no longer changes with more iterations and overall balances close (for a steady flow simulation). Convergence is not the same as accuracy and the solution is accurate if it matches experimental data. The entire simulation grid converged at less than fifty iterations. RESULTS AND DISCUSSION In this study, the result of velocity profiles is analyzed by the CFD postprocessor. The velocity profile has been simulated at the three different type of meshes and six different positions in the stenosis and without stenosis carotid bifurcation. The velocity profile for three different meshes is compared at the same position. On the other hand, the model geometry and density of meshes are observed in influencing the velocity profile. The position of velocity profile applies to non-stenotic and stenotic carotid bifurcation is shown in Figure 5. In the human body, there is a pair of common carotid artery (CCA) starts from the heart to ascending aorta then connect to the brain through Position 4 Position 2 ECA Position 1 Position CCA 7.5 Position 6 ICA Position 3 Figure 5: The position of velocity profile the neck. There are two branches at CCA, internal carotid artery (ICA) and external carotid artery (ECA). In the flow simulation, the Re at the CCA is 236. At the branch, ICA is 393 and 247, respectively, while ECA is 33 and 271, respectively. The result of the velocity profiles for without stenosis carotid bifurcation are compared with three different meshes at CCA are shown in Figure 6. The result shows the velocity profile of the three different meshes are similar to each other and the variance is less than 1%. The velocity profile flattens at the centre of the wall because influence by the centerline radius of curvature between ICA and ECA. The difference in mesh density did not influence these profiles. 7

8 vs Position Position 1 CCA_1 CCA_2 CCA_3 Figure 6: profiles in CCA at Re=236, from the flow simulation Re=294 Velecity vs Position Position 2 ECA_1 ECA_2 ECA_3 Figure 7(a): profiles in ECA at Re=33, from the flow simulation Re=13 as inlet velocity.1m/s vs Position Postition 4 ECA 1 ECA 2 ECA 3 Figure 7(b): profiles in ECA at Re=33, from the flow simulation Re=141 as inlet velocity.1m/s In Figure 7(a) and (b), shows the result of velocity profile for without stenosis carotid bifurcation are compared with three different meshes at two different positions at ECA. The velocity profile for mesh 3 (ECA 3) slightly skewed to the left wall compare to mesh 1 (ECA 1) and mesh 2 (ECA 2). The velocity profile of position 4 is taken exactly after the curvature between ICA and ECA and this has influence the pattern of the flow. The velocity profile improved as the flow towards the centre of the ECA. The variance is less than 15%. The difference in mesh density did not influence these profiles. 8

9 vs Position 3 1.2E-1 1.E-1 8.E-2 6.E-2 4.E-2 2.E-2.E Position 3 ICA_1 ICA_2 ICA_3 Figure 8(a): profiles in ICA at Re=247, from the flow simulation Re=191 as inlet velocity.1m/s vs Position Position 5 ICA_1 ICA_2 ICA_3 Figure 8(b): profiles in ICA at Re=331, from the flow simulation Re=149 as inlet velocity.1m/s vs Position Position 6 ICA_1 ICA_2 ICA_3 Figure 8(c): profiles in ICA at Re=393, from the flow simulation Re=165 as inlet velocity.1m/s In Figure 8(a), (b) and (c), shows the result of velocity profile for without stenosis carotid bifurcation are compared with three different meshes at three different positions in ICA. The velocity profiles pattern has improved as the flow passing through the maximum diameter and toward the end of ICA. The variance is 1 to 2%. However the flow did not influence by the density of mesh. The velocity at position 5 is exactly after the curvature between ICA and ECA and this has influence the pattern of the flow. 9

10 vs Position Position 1 CCA_1 CCA_2 CCA_3 Figure 9: profiles in CCA at Re=236, from the flow simulation Re=294 as inlet velocity.1m/s In Figure 9, shows the result of the velocity profiles for stenosis carotid bifurcation are compared with three different meshes at CCA. The result shows the velocity profile of the three different meshes are similar to each other and the variance is less than 1%.The velocity profile flattens at the centre of the wall because influence by the centerline radius of curvature between ICA and ECA. The difference in mesh density did not influence these profiles. At this position, the stenotic at ICA bulb did not influence the flow pattern. vs Position Position 2 ECA_1 ECA_2 ECA_3 Figure 1(a): profiles in ECA at Re=33, from the flow simulation Re=13 as inlet velocity.1m/s vs Position Position 4 ECA_1 ECA_2 ECA_3 Figure 1(b): profiles in ECA at Re=33, from the flow simulation Re=141 as inlet velocity.1m/s In Figure 1(a) and (b), shows the result of velocity profile for stenosis carotid bifurcation are compared with three different meshes at two different positions at ECA. The velocity profile for mesh 3 (ECA 3) slightly skewed to the left wall compare 1

11 to mesh 1 (ECA 1) and mesh 2 (ECA 2). The velocity profile of position 4 is taken exactly after the curvature between ICA and ECA and this has influence the pattern of the flow. The velocity profile improved as the flow towards the centre of the ECA. The variance is less than 15%. The difference in mesh density did not influence these profiles. At this position, the stenosis at ICA bulb did not influence the flow pattern. vs Position Position 3 ICA_1 ICA_2 ICA_3 Figure 11(a): profiles in ICA at Re=247, from the flow simulation Re=191, as inlet velocity.1m/s vs Position Position 5 ICA_1 ICA_2 ICA_3 Figure 11(b): profiles in ICA at Re=331, from the flow simulation Re=149 as inlet velocity.1m/s Vs Position E-2-1.E-2-5.E-3.E+ 5.E-3 1.E-2 Position 6 ICA_1 ICA_2 ICA_3 Figure 11(c): profiles in ICA at Re=2, from the flow simulation Re=136 as inlet velocity.1m/s In Figure 11(a), (b) and (c), shows the result of velocity profile for stenosis carotid bifurcation are compared with three different meshes at three different positions in ICA. The velocity profiles pattern has improved as the flow passing through toward the end of ICA. However, the velocity profile shown in Figure 11(c) referring to mesh 2 (ICA 2) and mesh 3 (ICA 3) at position 6, produced a flat line and result only shows at the beginning and toward the end of position 6. This result has 11

12 prove that the density of mesh influence the result of velocity profile and agreed with the statement from CFD manual [4]. Although fine grids are more accurate, sometimes it is less stable. Mesh 1 (ICA 1) shows the best result at any position and the mesh associated with the above statement (Figure 12). The variance is 1 to 2%. The velocity at position 5 is exactly after the curvature between ICA and ECA and this has influence the pattern of the flow. In Figure 13(a) and (b), show the result of wall shear stress at wall 4 and 5 for without stenosis and stenosis carotid bifurcation. Wall 4 is from the ECA wall and wall 5 is from the ICA wall as refer to boundary conditions. (a) (c) Figure 12(a): Mesh 1 of carotid bifurcation which produces the best result for without stenosis. (b) The velocity vectors of Mesh 1 (c): Contour of velocity magnitude (b) (d) (f) Figure 12(d): Mesh 1 of carotid bifurcation which gives the best result for stenosis. (e) The velocity vectors of Mesh 1 (f): Contour of velocity magnitude (e) CONCLUSIONS The three mesh types of carotid bifurcation have been designed to simulate the flow using computational fluid dynamics (CFD) based on numerical procedure. The simulation has been done on the carotid bifurcation without stenosis and stenosis. In this analysis Gambit is applied to build and mesh model for CFD. 12

13 FLUENT is used to simplify the geometry modeling and mesh generation process. All the iterative/numerical solution procedure may only give a solution which is converged relative to some criteria and the solution is accurate if it matches experimental data. The type of flow requirement is a two dimensional steady blood flow with Reynolds Number (Re) in the range of 2 to 4. Furthermore, the purposed of this analysis is to study the flow from the CFD post-processor and understand the influence of model geometry changing to the flow patterns. Overall results show a good flow patterns except for position 6 with stenosis. The present study provides further evidence that the mesh density influence the flow pattern. In producing a good mesh, the double-sided grading is chosen at vertical faces is to condense the elements near the wall so that it could solve the large velocity gradient in the boundary layer. The quality of the grid in any CFD problem is a major contributor to the quality of the solution [4]. However the computed results of Re does not agree with the experimental data of Re. REFERENCE [1]Jamie, D.,Steven, M., Jonathan, E., 1996, Prevention of stroke caused by carotid bifurcation stenosis-includes patient information sheet, American Family Physician.,pp.1 [2]Shigeru,T.,John,M.(24), Hemodynamics in a Carotid Bifurcation, Fluent.,pp.1 [3]Changsung,SK.,Cetin, K.,Dochan, K.,David,T.(26), Numerical Simulation of Local Blood Flow in the Carotid and Cerebral Arteries Under Altered Gravity, ASME.,pp [4]Mokhtarzadeh, R.,Natarajan, S.,(26/27), Introductory Manual for the CFD Finite Volume Program FLUENT and the MESH Generator GAMBIT, Mechanical Engineering.,pp [5] Fluent,(26) Gambit-Computational Fluid Dynamics (CFD) Preprocessor [online]available: Accessed 22/11/6 13