本研究利用質點軌跡流場觀察法(PTFV)與質點影像速度儀(PIV)，針對人體具有三支分支血管(壁頭動脈(brachiocephalic artery)、左頸總動脈(left common carotid artery)及左鎖骨下動脈(left subclavian artery))之主動脈弓進行研究。於主動脈弓之不同位置安裝支架(stent)，探討支架對主動脈弓與其分支血流及管壁剪應力的影響。為了簡化實驗的複雜度，採用透明玻璃製成之主動脈弓硬彎管模型，工作流體為水與甘油的混合物，黏度大約與血液相等，並將工作流體視為牛頓流體，流場溫度維持正常體溫37ºC，僅忽略血管的彈性及血管的錐度，降低影響實驗因素。使用血液泵(blood pump)輸出心臟脈波，頻率為1.2 Hz，Womersley parameter為16.28。觀察管內流場在時間與空間之結構衍化，並量測速度與壁面剪應力分佈。結果顯示，支架對於主動脈弓及其三支分支血管在流場結構、速度分佈及壁面剪應力等有很大的影響力。在正常主動脈弓模型(Type 1)中，主動脈弓與分支管交接處所受到的壁面剪應力最小，加上降胸主動脈之分離流對內側壁面的衝擊，造成低密度膽固醇(LDL)容易在此區聚集產生動脈硬化脂肪塊，使得管路窄縮而影響血流量，提高人體產生暈眩、昏迷甚至死亡的危險。支架置於主動脈弓入口端模型(Type 2)在主動脈弓與左頸總動脈及左鎖骨下動脈交接處，仍存在血管窄縮(stenosis)的危險；此外，受心臟脈波收縮與舒張週期影響，造成壁面剪應力的震盪，增加管壁受損的危險。支架置於降主動脈模型(Type 4)不僅可以降低整體主動脈弓及其三支主要分支血管的壁面剪應力，減少高剪應力作用管壁，使血管內層組織被破壞，進而演化成動脈瘤剝離的危險；且其分支管之剪應力不易隨心搏脈動而振盪。透過根均方邊壁剪應力分佈可看出，不管是主動脈弓內、外側、主動脈弓分支管之左、右側等，其無因次剪應力振盪範圍均在0.1以內，相對於其他模型(Type)都非常小，減少血管受到損傷的機會。

The pulsatile flow characteristics in a human stent aortic arch has been studied experimentally using particle tracking flow visualization method (PTFV) and the particle image velocimeter (PIV). Such an aortic arch is modeled using transparent Plexiglas U-tube with three main branches (brachiocephalic artery, left common carotid artery, and left subclavian artery) while the working fluid used to mimic the blood is a mixture by water and glycerol. Pulsatile flows simulating the output of a human heart beat is supplied by a “pulsatile blood pump”. The results of this study are obtained using a 72 strokes/minute (1.2 Hz) stroke rate, a 70 ml/stroke (5 L/minute) stroke volume, and a 45% / 55% systole/diastole ratio. The temperature, Womersley parameter and time-averaged Reynolds number are set at 37oC, 16.28 and 1148 respectively. The temporal/spatial evolution processes of the flow pattern, velocity distribution, and wall shear stress during systolic and diastolic phases are presented and discussed. During the systole phase, the boundary layer at the inner wall separates from the area near the turning arch where the thoracic aorta descends. The induced reverse flow increases the probability of plaque deposition while the strong reverse flow during diastolic phase is produced in the arch. Measured shear stresses show low values around the branch junctions and particularly high values around the outer wall of ascending aorta and descending thoracic aorta. These results showed a potential risk of atherosclerosis around the junctions of the three branches and aneurysms at the outer wall of ascending aorta. The benefit of placing the stent at the descending thoracic aorta is the decrease of wall shear stress along the aortic arch and three main branches. Furthermore, shaking of wall shear stress decreases with time during systole and diastole cycle due to the present of stent. The present result would be useful for further improvements in placing of stent technology.

[1] DeBakey, M. E., Lawrie, G. M., Glaeser, D. H., “Patterns of atherosclerosis and their surgical significance,” Annals of Surgery, Vol. 201, No. 2, 1985, pp. 115-131.
[2] Abrams, J., “Chronic stable angina, “The New England Journal of Medicine, Vol. 352, No. 24, 2005, pp. 2524-2533.
[3] Kim, M., Taulbee, D. B., Tremmel, M., Meng, H. “Comparison of two stents in modifying cerebral aneurysm hemodynamics,” Journal of Biomedicine Engineering, Vol. 36, No. 5, 2008, pp. 726-741.
[4] Liou, T. M., Liou, S. N., Chu, K. L., “Intra-aneurysmal flow with helix and mesh stent placement across side-wall aneurysm pore of a straight parent vessel,” Journal of Biomechanical Engineering, Vol. 126, February 2004, pp. 36-43.
[5] Liou, S. N., Liou, T. M., “Pulsatile flows in a lateral aneurysm anchored on a stented and curved parent vessel,” Experimental Mechanics, Vol. 44, No. 3, 2004, pp. 253-260.

[6] Fung, G. S. k., Lam, S. K., Cheng, S. W. K., Chow, K. W., “On stent-graft models in thoracic aortic endovascular repair: acomputational investigation of the hemodynamic factors,” Computers in Biology and Medicine, Vol. 38, January 2008, pp. 484-489.
[7] Lieber, B. B., Livescu, V., Hopkins, L. N., Wakhloo, A. K., “Particle image velocimetry assessment of stent design Influence on Intra-aneurysmal Flow,” Annals of Biomedical Engineering, Vol. 30, No. 6, 2002, pp. 768-777.
[8] Yu, S. C. M. and Zhao, J. B., “A steady flow analysis on the stented and non-stented sidewall aneurysm models,” Medical Engineering & Physics, Vol.21, No. 3, 1999, pp. 133-141.
[9] Yu, S. C. M., “Steady and pulsatile flow studies in Abdominal Aortic Aneurysm models using Particle Image Velocimetry,” International Journal of Heat and Fluid Flow, Vol. 21, No. 1, 2000, pp. 74-83.

[10] Ku, D. N., “Blood flow in arteries,” Annual Review of Fluid Mechanics, Vol. 29, No. 1, 1997, pp. 399-434.
[11] Kang, S. G., Tarbell, J. M., “The impedance of curved artery models,” J. Biomechanical Engineering, Vol. 105, August 1983, pp. 275-282.
[12] Kjernes, M., Svindland, A., Walloe, L., Wille, S. O., “Localization of early atherosclerotic lesions in an arterial bifurcation in humans,” Acta. path. microbiol. scand. Sect. A, Vol. 89, August 1981, pp. 35-40.
[13] Malek, A. M., Alper, S. L., Izumo, S., “Hemodynamic shear stress and its role in atherosclerosis,” Journal of the America Medical Association, Vol. 282, No. 21, 1999, pp. 2035-2042.
[14] Nerem, R. M., Cornhill, J. F., “The role of fluid mechanics in atherogenesis,” J. Biomechanical Engineering, Vol. 102, August 1980, pp. 181-189.
[15] Lei, M., Kleinstreuer, C., Truskey, G. A., “Numerical investigation and prediction of atherogenic sites in branching arteries,” J. Biomechanical Engineering, Vol. 117, August 1995, pp. 350-357.
[16] Pei, Z.-H., Xi, B.-S., Hwang, H. C., “Wall shear stress distribution in a model human aortic arch: assessment by an electrochemical technique,” J. Biomechanics, Vol. 18, No. 9, 1985, pp. 645-656.
[17] Ku, D. N., Giddens, D. P., Zarins, C. K., Glagov, S., “Pulsatile flow and atherosclerosis in the human carotid bifurcation – positive correlation between plaque location and low and oscillating shear stress,” Arteriosclerosis, Vol. 5, February 1985, pp. 293-301.
[18] Naruse, T., Tanishita, K., “Large curvature effect on pulsatile entrance flow in a curved tube: model experiment simulating blood flow in an aortic arch,” J. Biomechanical Engineering, Vol. 118, May 1996, pp. 180-186.
[19] Choi, U. S., Talbot, L., Cornet, I., “Experimental study of wall shear rates in the entry region of a curved tube,” J. Fluid Mech., Vol. 93, No. 3, 1979, pp. 465-489.

[20] Singh, M. P., Sinha, P. C., Aggarwal, M., “Flow in the entrance of the aorta,” J. Fluid Mech., Vol. 87, No. 1, 1978, pp. 97-120.
[21] Pedley, T. J., “Viscous boundary layers in reversing flow,” J. Fluid Mech., Vol. 74, No. 1, 1976, pp. 59-79.
[22] Rodkiewicz, C. M., Kalita, W., Kennedy, J. S., Pelot, R., “On the flow field distortions due to the aortic arch twist,” J. Biomechanics, Vol. 18, No. 10, 1985, pp. 781-787.
[23] Chandran, K. B., Yearwood, T. L., Wieting, D. W., “An experimental study of pulsatile flow in curved tube,” J. Biomechanics, Vol. 12, No. 10, 1979, pp. 793-805.
[24] Tada, S., Oshima, S., Yamane, R., “Classification of pulsating flow patterns in curved pipes,” J. Biomechanical Engineering, Vol. 118, August, August 1996, pp. 311-317.
[25] Yearwood, T. L., Chandran, K. B., “Experimental investigation of steady flow through a model of the human aortic arch,” J. Biomecanics, Vol. 13, April 1980, pp. 1075-1088.
[26] Chandran, K. B., Yearwood, T. L., “Experimental study of Physiological pulsatile flow in a curved tube,” J. Fluid Mech., Vol. 111, January 1981, pp. 59-85.
[27] Yearwood, T. L., Chandran, K. B., “Physiological pulsatile flow experiments in a model of the human aortic arch,” J. Biomechanics, Vol. 15, No. 9, 1984, pp. 683-704.
[28] Khalighi, B., Chandran, K. B., Chen, C.-J., “Steady flow development past valve prostheses in a model human aorta–I. Centrally occluding valves,” J. Biomechanics, Vol. 16, No. 12, 1983, pp. 1003-1011.
[29] Chandran, K. B., Cabel, G. N., Khalighi, B., Chen, C.-J., 1984. “Pulsatile flow past aortic valve bioprostheses in a model human aorta.” J. Biomechanics, Vol. 17, No. 8, pp. 609-619.
[30] Chandran, K. B., Khalighi, B., Chen, C.-J., “Experimental study of physiological pulsatile flow past valve prostheses in a model of human aorta–I. Caged ball valves,” J. Biomechanics, Vol. 18, No. 10, 1985, pp. 763-772.
[31] Chandran, K. B., Khalighi, B., Chen, C.-J., “Experimental study of physiological pulsatile flow past valve prostheses in a model of human aorta–II. Tilting disc valves and the effect of orientation,” J. Biomechanics, Vol. 18, No. 10, 1985, pp. 773-780.
[32] Khalighi, B., Chandran, K. B., Chen, C.-J., “Steady flow development past valve prostheses in a model human aorta–II. Tilting disc valves,” J. Biomechanics, Vol. 16, No. 12, 1983, pp. 1013-1018.
[33] Nandy, S., Tarbell, J. M., “Measurement of wall shear stress distal to a tri-leaflet valve in a rigid model of the aortic arch with branch flows,” J. Biomechanical Engineering, Vol. 110, August 1988, pp. 172-179.
[34] Dean, W. R., “Note on the motion of fluid in a curved pipe,” Philos. Mag., Vol. 7, No. 4, 1928, pp. 208-223.
[35] Adrian, R. J., “Particle-imaging techniques for experimental fluid mechanics,” Annual Review of Fluid Mech., Vol. 23, January 1991, pp. 261-304.
[36] Keane, R. D., Adrian, R. J., “Theory of cross-correlation analysis of PIV images,” Applied Scientific Research, Vol. 49, No. 3, 1992, pp. 191-215.
[37] Fry, D. L., “Certain Histological and Chemical Responese of the Vascular Interface to Acutely Induced Mechanical Stress in the Arota of the Dog,” circulation Rch., Vol. 24, January 1969, pp. 93-108.
[38] Caro, C. G. Fitz-Gerald, J. M. and Schroter, R. C., “Atheroma and Arterial Wall Shear observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis,” Proc. R. Soc. Lond., Vol. 177, February 1971, pp. 109-159.
[39]Gessner, F. B., “Hemodynamic Theories of Atherogenesis,Criculation Research,” circulation Rch., Vol. 33, No. 3, 1973, pp. 259-266.

[40] Adams, E. W., Johnston, J. P., “Flow structure in the near-wall zone of a turbulent separated flow,” AIAA J., Vol. 26, No. 8, 1988, pp. 932-939.
[41] Bejan. A., Convection Heat Transfer, John Wiley & Sons, New York, 1984, pp. 227-278.

[42] Clauser, F. H., “Turbulent boundary layers in adverse pressure
gradients,” Journal of the Aeronautical Sciences, Vol. 21, February 1954, pp.91-108.
[43] Huang, P. G., Bradshaw, P., “Law of the wall for turbulent flows in pressure gradients,” AIAA J., Vol. 33, No. 4, 1995, pp. 624-632.
[44] Gonzalez C. F., Cho Y. I., Ortega H. V., and Moret J., “Intracranial Aneurysms: flow analysis of their oring and progression,” America Journal of Neuroradiology, Vol. 13, No. 1, 1992, pp. 181-188.
[45] Guo W., Liu X., Liang F., Yang D., Zhang G., Sun L., Song Q., Zhao S., and Gai L., “Transcarotid artery endovascular reconstruction of the aortic arch by modified bifurcated stent graft for Stanford Type A dissextion,” Asian Journal of Surgery, Vol. 30, No. 4, 2007, pp. 290-295.
[46] Huang R. F., Yang T. F., Lan Y. K., “Pulsatile flows and wall-shear stresses in models simulating normal and stenosed aortic arches,” Experiments in Fluids, Vol. 48, No. 3, October 2010, pp. 497-508.
[47] Uchida, N., Lshihara, H., Shibamura, H., Kyo, Y., Ozawa, M., “Midterm results of extensive primary repair of the thoracic aorta by means of total arch replacement with open stent graft placement for an acute Type A aortic dissection,” The Journal of Thoracic and Cardiovascular Surgery, Vol. 131, April 2006, pp. 862-867.
[48] Flores, J., Kunihara, T., Shiiya, N., Yoshimoto, K., Matsuzaki, K., Yasuda, K., “Extensive deployment of the stented elephant trunk is associated with an increased risk of spinal cord injury,” The Journal of Thoracic and Cardiovascular Surgery, Vol. 131, No. 2, 2006, pp. 336-342.
[49] Palmaz, J. C., Sibbitt, R. R., Reuter, S. R., Tio, F. O., Rice, W. J., “Expandable Intraluminal Graft A Preliminary Study,” Radiology, Vol. 156, November 1985, pp. 73-77.
[50] Nichols, W. W., O’rourke, M. F., McDonald’s Blood Flow in Arteries Theroretical, Experimental and Clinical Principles, 5th edition, Hodder Arnold, London, UK, 2005.
[51] 彭楷瑜(編譯)，漫畫心臟血管系統，合記圖書出版社, 2003.