1242 Fig. 2 Schematic illustration of vessel models. Model A: Cylinder model (ø 5 mm) Model B: The stenosis model has a narrow region (ø 2.5 mm) in th

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1 1241 ノート Computational Fluid Dynamics: CFD , 2 佐保辰典 1 大西英雄 3 杉原利彦 2 中村義隆 2 湯田逸雄 Code Nos , 緒言 25.4 wall shear stress: WSS 1 4 WSS computational fluid dynamics: CFD WSS 5 CFD CFD CFD CFD 6 8 CFD Tackling Hemodynamic Analysis of the Carotid Artery Using Open-source Software and Computational Fluid Dynamics Tatsunori Saho, 1, 2 Hideo Onishi, 1 Toshihiko Sugihara, 3 Yoshitaka Nakamura, 2 and Itsuo Yuda 2 1 Program in Health and Welfare, Graduate on School of Comprehensive Scientific Research, Prefectural University of Hiroshima 2 Department of Radiological Technologist, Kokura Memorial Hospital 3 SystemCRAFT Co., Ltd. Received May 13, 2013; Revision accepted September 17, 2013 Code Nos. 261, 500, 1030 Summary Purpose: The aim of this study was to evaluate the impact of wall share stress (WSS) in the carotid artery using a computed fluid dynamics analysis system and adopting open-source software. Methods: The dependence of element number (computation time and analytical accuracy) were considered with simple vessel models. We evaluated WSS and flow velocity using a carotid artery model that was based on the outcome of simple vessel models. Results: When the number of elements was 10 5 or more, the flow velocity error of the outlet decreased to 0.5% or below when using simple vessel models. The carotid bifurcation model showed a whirlpool and a decrease in flow velocity in the carotid bulb part. Conclusion: An analysis system was built using open source software. The results from the carotid bifurcation model suggested that hemodynamics contributes to the development of carotid stenosis. Key words: computational fluid dynamics, open-source software, magnetic resonance angiography, wall share stress *Proceeding author

2 1242 Fig. 2 Schematic illustration of vessel models. Model A: Cylinder model (ø 5 mm) Model B: The stenosis model has a narrow region (ø 2.5 mm) in the center Fig. 1 CFD CFD WSS 9, 10 magnetic resonance image: MRI phase contrast MR angiography PC-MRA PC-MRA CFD CFD MRA Flowchart of CFD analysis. Import analysis model: STL-formatted; mesh generated using OpenFOAM; boundary conditions determined using Helyx OS; analysis model: SimpleFoam, results visualized using Paraview. 1. 方法 1-1 CFD CFD MacBookPro Apple Inc., California, USA CFD OpenFOAM Open CFD Ltd., Bracknell, UK Linux Mac OS Linux CFD OpenFOAM CFD OpenFOAM graphical user interface GUI Helyx OS Engys Ltd., London, UK Paraview Kitware Inc., New York, USA Fig. 1 OpenFOAM 1-2 CFD threedimensional 3D Blender Blender Foundation, Amsterdam, Netherlands OpenFOAM 2 Fig. 2 A 5 mm 50 mm B 5 mm 50 mm 2.5 mm 15 mm Osirix Osirix Foundation, California, USA Blender Osirix MRA

3 1243 Table 1 Boundary conditions Object Inlet Outlet u (m/s) p (m 2 /s 2 ) u (m/s) p (m 2 /s 2 ) Vessel model (A) 0.5 zero gradient zero gradient 0 fixed wall, no slip (B) 0.5 zero gradient zero gradient 0 fixed wall, no slip Carotid bifurcation 0.5 zero gradient zero gradient 0 fixed wall, model (at infinity) no slip Wall Fig. 3 An illustration of the carotid bifurcation model used for MRA imaging. The model has a single inlet (ø 8 mm) and two outlets (ø 5 mm, ø 6 mm); total length is 50 mm. a b c d e f stereolithography STL Fig mm common carotid artery: CCA 1 internal carotid artery: ICA 2 external carotid artery: ECA 8 mm 6 mm 5 mm 1-3 CFD Table 1 11 u=0.5 m/s p=0 m 2 /s 2 12 ρ=1050 kg/m 3 η= Pa s Fig. 4 Comparison of local flow velocity estimated from simple vessels in Figure 2 as a function of number of elements [(a) 1050, (b) 8000, (c) 63200, (d) , (e) , and (f) 4386 and five added layers]. SimpleFoam semi implicit method for pressure-linked equations SIMPLE CFD A Fig. 4 a 1050 b 8000 c d e A a e 1 f a B Fig. 5 a 5560 b c

4 1244 Fig. 5 d e A a f B a e Fig. 1 generate mesh 1-5 CFD A 25 mm CFD A m 3 /s 1-6 CFD a b c d e Comparison of local flow velocity estimated from stenosis vessels in Figure 2 as a function of number of elements [(a) 5560, (b) 43496, (c) , (d) , (e) )]. CFD Fig. 6 Scheme of wall segmentations (inner wall of the external carotid artery: inner ECA, outer wall of the external carotid artery: outer ECA, inner wall of the ICA: inner ICA, outer wall of the ICA: outer ICA, and divider wall) for the carotid bifurcation model studied in Figure inner ICA outer ICA inner ECA outer ECA divider wall Fig. 6 ICA ECA inner outer divider wall 2. 結果 2-1 Fig. 7 CFD A outlet c d e Fig. 8 B 2-2 CFD Fig. 9 CFD Fig. 4 5 A B Fig. 4 A outlet inlet Inlet

5 1245 Fig. 7 Mesh generation estimated from simple vessels in Fig. 2 as a function of number of elements [(a) 1050, (b) 8000, (c) 63200, (d) , (e) , and (f) 4386 and five added layers]. a b c d e f Fig. 8 Mesh generation time as a function of number of elements. Increasing the number of elements increases mesh generation time, as with involution. Fig. 9 Plot of model solving time as a function of number of elements. Solving time and number of elements were approximated using a linear function m/s 25 mm Fig. 10 a 0 m/s 5 f a Fig. 5 B a 10 5 c d e Table CFD Fig. 11 CFD 377 s a divider wall b c

6 1246 Fig. 10 Flow velocity profile and theoretical value. The 1050-element model did not detect flow velocity of 0 m/s near the surface of wall. The flow velocity of the central part in each model increased under the boundary condition of >0.5 m/s in the inlet plane. Table 2 Number of elements Accuracy of flow volume at outlet plane Flow volume (m 3/s) Add layer Relative error (%) (Theoretical value m3/s) Fig. 11 Pressure vector (a), velocity stream line (b), and velocity distribution (c) predicted by CFD for the carotid bifurcation model. Very high pressure is applied to the divider wall, whirlpool flow is found at the bifurcation, and low velocity was observed at the ICA and ECA outer walls. a b c 日本放射線技術学会雑誌

7 1247 outer ICA outer ECA 3. 考察 CFD 1 4 Osirix MRA CFD CFD CFD OpenFOAM BlockMesh SnappyHexMesh CFD Table Fig. 8 CFD BlockMesh SnappyHexMesh 18 Fig m/s Fig. 4 f 0 m/s Fig. 4 f Fig. 4 c 59.5 s 89.7 Fig. 4 f Fig. 7 outlet Fig. 5 d e , ECA ICA 0 m 2 /s 2

8 ICA divider wall Fig. 11 a WSS 21 WSS WSS divider wall WSS Papathanasopoulou 9 WSS Fig. 11 c outer ICA outer ECA Marshall 10 Fig. 11 b 3 Fig. 7 in vivo 4. 結語 CFD CFD in vivo 謝辞 CFD CAE

9 1249 参考文献 1 Groen HC, Simons L, van den Bouwhuijsen QJ, et al. MRIbased quantification of outflow boundary conditions for computational fluid dynamics of stenosed human carotid arteries. J Biomech 2010; 43(12): ; 23(249): Yang C, Canton G, Yuan C, et al. Advanced human carotid plaque progression correlates positively with flow shear stress using follow-up scan data: an in vivo MRI multipatient 3D FSI study. J Biomech 2010; 43(13): Seong J, Lieber BB, Wakhloo AK. Morphological agedependent development of the human carotid bifurcation. J Biomech 2005; 38(3): ; 44(3): ; 28(4): In Vivo BIO Clinica 2012; 27(12): Steelman SM, Wu Q, Wagner HP, et al. Perivascular tethering modulates the geometry and biomechanics of cerebral arterioles. J Biomech 2010; 43(14): Papathanasopoulou P, Zhao S, Köhler U, et al. MRI measurement of time-resolved wall shear stress vectors in a carotid bifurcation model, and comparison with CFD predictions. J Magn Reson Imaging 2003; 17(2): Marshall I, Zhao S, Papathanasopoulou P, et al. MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models. J Biomech 2004; 37(5): Hyun S, Kleinstreuer C, Archie JP. Computational analysis of effects of external carotid artery flow and occlusion on adverse carotid bifurcation hemodynamics. J Vasc Surg 2003; 37(6): CFD 2011; 10: Yamamoto S, Maruyama S, Nakahara Y, et al. Computational Flow Dynamics in Abdominal Aortic Aneurysm Using Multislice Computed Tomography. 2006; 62(1): Holman JP. Heat Transfer. Boston: McGrow-Hill, OpenCFD Foundation. OpenFOAM Users Guide. USA: OpenCFD Foundation: : BRAIN MEDICAL 2011; 23(1): FLOPS 2012; 53(8): ; 61(589): ; 32(10): ; 26(2):

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