本研究利用質點軌跡流場觀察法(PTFV)與質點影像速度儀(PIV)，針對主動脈弓彎管模型進行流場診測，探討動脈粥狀硬化斑所造成的管路窄縮對主動脈弓血流的影響。三種不同主動脈弓模型的窄縮率分別為0%、25%及50%，使用血液脈動泵輸出心臟脈動波搭配兩種不同的脈動頻率，分別為f = 0.5Hz與f = 1.2Hz，Womersley number為9.02 與13.97。觀察管內流場之結構衍化以及量測速度、壁面剪應力和壁面垂直應力的分佈。並利用壁面定律(law of wall)驗證此套PIV後處理軟體，在徑向速度很小的情況下，靠近壁面的計算規則符合此定律。在實驗中可觀察到，在心搏脈動波中，隨著脈動頻率的增加，流場衍化結構會發生時間延後的現象。在心搏脈動波收縮行程中，當管路拱型區窄縮率越高時，管路的紊流臨界雷諾數就越低，流體經過硬化物發生分離現象的特徵時間會提前，分離點位置會延後。分離區從拱型區延伸至降胸主動脈內側壁面，分離區內的流場型態包含二次流、螺旋狀上升流以及渦漩逸放、渦漩拉伸的流場結構。在正常主動脈弓中，拱型區域中心截面內側壁面所受到的壁面剪應力最小，加上二次流往內側壁面的衝擊，造成脂肪斑塊容易在此區聚集產生動脈硬化脂肪塊，使得管路窄縮。在上升主動脈及降胸主動脈的內外側壁面剪應力較大。在管路即將轉彎處的外側壁面，承受較大的動量垂直分量衝擊，當血管組織發生病變彈性降低時，較容易產生動脈瘤。隨管路窄縮率升高，而窄縮區的剪應力也會劇烈的增加，此時強大的剪應力會作用在硬化物纖維狀的脂肪斑，與膠原蓋，破壞其組織。一旦組織被破壞，血小板將匯聚在此處並凝結形成血栓，導致血液中的氧氣與養分無法運送到器官造成器官機能衰竭、壞死。

flow characteristics and evolution processes in aortic arch models with atherosclerosis are diagnosed by using the particle tracking flow visualization method (PTFV) and the particle image velocimeter (PIV) over various experimental models and pulsating frequencies. These aortic arch models are made of transparent plexiglas U-tubes. The pulsating frequencies are set at 0.5 Hz and 1.2 Hz. Quantitative flow properties, e.g., the velocity vector maps, streamline patterns, axial velocity, wall shear-stress, and wall normal stress, are obtained by analyzing the measured PIV data. It is found that the flows evolve complicatedly into three dimensional structures during the processes of acceleration, deceleration, and reversing. During systole stroke, the boundary layer on the inner wall separates from the area near the turning arch to the descending thoracic aorta and three dimensional secondary flows are observed. These characteristic flow structures induce reverse and low speed flows and therefore would increase the probability of plaque deposition around the inner wall of the arch. When the stenosis increases, the separation point would be deferred a little to the downstream area and the timing for separation would be advanced. During the systole stroke, the normal impulse component developed in the flow in the regions around the up- and downstream turning arches of the outer tube-wall are relatively high. During the diastolic process, strong reversed flow is produced along the inner walls of curvature. In the aortic arch model without the atherosclerosis, the maximum wall shear stress appears on the inner and outer walls of the ascending aorta, which implies that the aortic dissection would be occurring there most likely. In the aortic arch model with the atherosclerotic, the maximum wall shear stress appears on the inner wall of the arch might crack fibrolipid plaque and collagenous cap of atherosclerotic plaque and therefore would induce rapid assembling of platelets on the exposed connective tissues, form the thrombosis, and therefore diminish the transport of oxygen and metabolites to the organs.

[1] Ku, D. N., “Blood flow in arteries,” Annual Review of Fluid Mechanics, Vol. 29, January 1997, pp. 399-434.
[2] Shemer, L., Wygnanski, I., and Kit, E., “Pulsatile flow in a pipe,” Journal of Fluid Mechanics, Vol. 153, 1985, pp. 313-337.
[3] He, X. and Ku, D. N., “Unsteady Entrance Flow Development in a Straight Tube,” Journal of Biomechanical Engineering, Vol. 116, August 1994, pp. 355-361.
[4] 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, April 1999, pp. 133-141.
[5] 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, February 2000, pp. 74-83.
[6] Steinman, D. A., Poepping, T. L., Tambasco, M., Rankin, R. N., and Holdsworth, D. W., “Flow patterns at the Stenosed Carotid Bifurcation: Effect of Concentric versus Eccentric Stenosis,” Annals of Biomedical Engineering, Vol. 28, No. 4, 2000, pp. 415-423.
[7] Steinman, D. A., “Simulated pathline visualization of computed periodic blood flow patterns,” Journal of Biomechanics, Vol. 33, May 2000, pp. 623-628.
[8] Zhao, S. Z., Xu, X. Y., Hughes, A. D., Thom, S. A., Stanton, A. V., Ariff, B., and Long, Q., “Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation,” Journal of Biomechanics, Vol. 33, August 2000, pp. 975-984.
[9] Zhao, S. Z., Ariff, B., Long, Q., Hughes, A. D., Thom, S. A., Stanton, A. V., and Xu, X. Y., “Inter-individual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans,” Journal of Biomechanics, Vol. 35, October 2002, pp. 1367-1377.
[10] Perktold, K., Hofer, M., Rappitsch, G., Loew, M., Kuban, B. D., and Friedman, M. H., “Validated computation of physiologic flow in a realistic coronary artery branch,” Journal of Biomechanics, Vol. 31, December 1998, pp. 217-228.
[11] Pivkin, I. V., Richardson, P. D., Laidlaw, D. H., and Karniadakis, G. E., “Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model,” Journal of Biomechanics, Vol. 38, June 2005, pp. 1283-1290.
[12] Zhao, Y., Brunskill, C. T., and Lieber, B. B., “Inspiratory and Expiratory Steady Flow Analysis in a Nodel Symmetrically Bifurcating Airway,” Journal of Biomechanics Engineering, Vol. 119, February 1997, pp. 52-58.
[13] Fresconi, F. E., Wexler, A. S., and Prasad, A. K., ”Expiration flow in a symmetric bifurcation,” Experiments in Fluids, Vol. 35, No. 5, 2003, pp. 493-501.
[14] DeBakey, M. E., Lawrie, G. M., Glaeser, and D. H., “Patterns of atherosclerosis and their surgical significance,” Annals of Surgery,
Vol. 201, No. 2, 1985, pp. 115-131.
[15] Abrams, J., “Chronic Stable Angina,” The New England Journal of Medicine, Vol. 352, June 2005, pp. 2524-2533.
[16] Nerem, R. M., “Vascular fluid mechanics, the arterial wall, and atherosclerosis,” Journal of Biomechanical Engineering, Vol. 114, August 1992, pp. 274-283.
[17] Berger, S. A., Jou, L-D., “Flows in Stenotic Vessels,” Annual Review of Fluid Mechanics, Vol. 32, January 2000, pp. 347-382.
[18] Long, Q., Xu, X. Y., Ramnarine, K. V., and Hoskins, P., “Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis,” Journal of Biomechanics, Vol. 34, October 2001, pp. 1229-1242.
[19] Lee, K. W. and Xu, X. Y., “Modelling of flow and wall behaviour in a mildly stenosed tube,” Medical Engineering & Physics, Vol. 24, November 2002, pp. 575-586.
[20] Varghese, S. S., Frankel, S. H., “Numerical Modeling of Pulsatile Turbulent Flow in Stenotic Vessel,” Journal of Biomechanical Engineering, Vol. 125, August 2003, pp. 445-460.
[21] Choi, U. S., Talbot, L., and Cornet, I., “Experimental study of wall shear rates in the entry region of a curved tube,” Journal of Fluid Mechanics, Vol. 93, part 3, 1979, pp. 465-489.
[22] Chandran. K. B., Yearwood, T. L., and Wieting, D. W., “An experimental study of pulsatile flow in a curved tube,” Journal of Biomechanics, Vol. 12, 1979, pp. 793-805.
[23] Tada, S., Oshima, S., and Yamane, R., “Classification of Pulsating Flow Patterns in Curved Pipes,” Journal of Biomechanical Engineering, Vol. 118, August 1996, pp. 311-317.
[24] Yearwood, T. L. and Chandran, K. B., “Experimental investigation of steady flow through a model of the human aortic arch,” Journal of Biomechanics, Vol. 13, 1980, pp. 1075-1088.
[25] Chandran, K. B. and Yearwood, T. L., “Experimental study of physiological pulsatile flow in a curved tube,” Journal of Fluid Mechanics, Vol. 111, January 1981, pp. 59-85.
[26] Yearwood, T. L. and Chandran, K. B., “Physiological pulsatile flow experiments in a model of the human aortic arch,” Journal of Biomechanics, Vol. 15, No. 9, 1984, pp. 683-704.
[27] Khalighi, B., Chandran, K. B., and Chen C. J., “Steady flow development past valve prostheses in a model human aorta-I. Centrally occluding valves,” Journal of Biomechanics, Vol. 16, No. 12, 1983, pp. 1003-1011.
[28] Khalighi, B., Chandran, K. B., and Chen C. J., “Steady flow development past valve prostheses in a model human aorta-Ⅱ. Tilting disc Valves,” Journal of Biomechanics, Vol. 16, No. 12, 1983, pp. 1013-1018.
[29] Chandran, K. B., Cabell, G. N., Khalighi, B., and Chen C. J., “Pulsatile flow past aortic valve bioprostheses in a model human aorta,” Journal of Biomechanics, Vol. 17, No. 8, 1984, pp. 609-619.
[30] Chandran, K. B., Khalighi, B., and Chen C. J., “Experimental study of physiological pulsatile flow past valve prostheses in a model of human aorta-I. Caged ball valves,” Journal of Biomechanics, Vol. 18, No. 10, 1985, pp. 763-772.
[31] Chandran, K. B., Khalighi, B., and 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,” Journal of Biomechanics, Vol. 18, No. 10, 1985, pp. 773-780.
[32] 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,” Journal of Biomechanical Engineering, Vol. 110, August 1988, pp. 172-179.
[33] Shancheraghi, N., Dwyer, H. A., Cheer, A. Y., Barakat, A. I., and Rutaganira, T., “Unsteady and three-Dimensional Simulation of Blood Flow in the Human Aortic Arch,” Journal of Biomechanical Engineering, Vol. 124, August 2002, pp. 378-387.
[34] Richard, C. F. and John, H. S., Fundamentals of air pollution engineering, New Jersey, 1988, pp. 290-357.
[35] Womersley, J. R., “Method for the calculation of velocity rate of flow and viscous drag in arteries when the pressure gradient is known,” Journal of Physiol., Vol. 127, 1955, pp. 553-563.
[36] Bejan, A., Convection Heat Transfer, Wiley, New York, 1984, pp. 238-241.
[37] Huang, P. G., and Bradshaw, P., “Law of the Wall for Turbulent Flows in Pressure Gradients,” AIAA Journal, Vol. 33, No. 4, 1995, pp. 624-632.
[38] Clauser, F. H., “Turbulent Boundaries in Adverse Pressure Gradient, ” Journal of the Aeronautical Sciences, Vol. 21, February 1954, pp. 91-108.
[39] 彭楷瑜(編譯),漫畫心臟血管系統,合記圖書出版社,2003.