A review on computational fluid dynamics modelling in human thoracic aorta
It has long been recognized that the forces and stresses produced by the blood flow on the walls of the cardiovascular system are central to the development of different cardiovascular diseases. However, up to now, the reason why arterial diseases occur at preferential sites is still not fully under...
- Autores:
-
Laín Beatove, Santiago
Caballero Gaviria, Andrés David
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2013
- Institución:
- Universidad Autónoma de Occidente
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- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
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- oai:red.uao.edu.co:10614/11806
- Acceso en línea:
- http://red.uao.edu.co//handle/10614/11806
- Palabra clave:
- Aorta, Thoracic
Flujo sanguíneo
Hemodinámica
Blood flow
Hemodynamics
Blood flow
Computational fluid dynamics
Hemodynamics
Human thoracic aorta
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- openAccess
- License
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A review on computational fluid dynamics modelling in human thoracic aorta |
| title |
A review on computational fluid dynamics modelling in human thoracic aorta |
| spellingShingle |
A review on computational fluid dynamics modelling in human thoracic aorta Aorta, Thoracic Flujo sanguíneo Hemodinámica Blood flow Hemodynamics Blood flow Computational fluid dynamics Hemodynamics Human thoracic aorta |
| title_short |
A review on computational fluid dynamics modelling in human thoracic aorta |
| title_full |
A review on computational fluid dynamics modelling in human thoracic aorta |
| title_fullStr |
A review on computational fluid dynamics modelling in human thoracic aorta |
| title_full_unstemmed |
A review on computational fluid dynamics modelling in human thoracic aorta |
| title_sort |
A review on computational fluid dynamics modelling in human thoracic aorta |
| dc.creator.fl_str_mv |
Laín Beatove, Santiago Caballero Gaviria, Andrés David |
| dc.contributor.author.none.fl_str_mv |
Laín Beatove, Santiago Caballero Gaviria, Andrés David |
| dc.subject.mesh.eng.fl_str_mv |
Aorta, Thoracic |
| topic |
Aorta, Thoracic Flujo sanguíneo Hemodinámica Blood flow Hemodynamics Blood flow Computational fluid dynamics Hemodynamics Human thoracic aorta |
| dc.subject.armarc.spa.fl_str_mv |
Flujo sanguíneo Hemodinámica |
| dc.subject.armarc.eng.fl_str_mv |
Blood flow Hemodynamics |
| dc.subject.proposal.spa.fl_str_mv |
Blood flow |
| dc.subject.proposal.eng.fl_str_mv |
Computational fluid dynamics Hemodynamics Human thoracic aorta |
| description |
It has long been recognized that the forces and stresses produced by the blood flow on the walls of the cardiovascular system are central to the development of different cardiovascular diseases. However, up to now, the reason why arterial diseases occur at preferential sites is still not fully understood. This paper reviews the progress, made largely within the last decade, towards the use of 3D computational fluid dynamics (CFD) models to simulate the blood flow dynamics and its interaction with the arterial wall within the human thoracic aorta (TA). We describe the technical aspects of model building, review methods to create anatomic and physiologic models, obtain material properties, assign boundary conditions, solve the equations governing blood flow , and describe the assumptions used in running the simulations. Detailed comparative information is provided in tabular format about the model setup, simulation results, and a summary of the major insights and contributions of each TA article reviewed. Several syntheses are given that summarize the research carried out by influential research groups, review important findings, discuss the methods employed, limitations, and opportunities for further research. We hope that this review will stimulate computational research that will contribute to the continued improvement of cardiovascular health through a strong interaction and cooperation between engineers and clinicians |
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2013 |
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2013-06 |
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2020-01-16T14:58:41Z |
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2020-01-16T14:58:41Z |
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Caballero, A.D., & Laín, S. (2013). A Review on Computational Fluid Dynamics Modelling in Human Thoracic Aorta. Cardiovascular Engineering and Technology, 4, 103-130. DOI: 10.1007/s13239-013-0146-6 |
| dc.identifier.uri.none.fl_str_mv |
http://red.uao.edu.co//handle/10614/11806 |
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10.1007/s13239-013-0146-6 |
| identifier_str_mv |
Caballero, A.D., & Laín, S. (2013). A Review on Computational Fluid Dynamics Modelling in Human Thoracic Aorta. Cardiovascular Engineering and Technology, 4, 103-130. DOI: 10.1007/s13239-013-0146-6 10.1007/s13239-013-0146-6 |
| url |
http://red.uao.edu.co//handle/10614/11806 |
| dc.language.iso.eng.fl_str_mv |
eng |
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eng |
| dc.relation.eng.fl_str_mv |
Cardiovascular Engineering and Technology. páginas 1-32 |
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130 |
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2 |
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103 |
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4 |
| dc.relation.ispartofjournal.eng.fl_str_mv |
Cardiovascular Engineering and Technology |
| dc.relation.references.none.fl_str_mv |
Mori D, Yamaguchi T. 2002a. Computational fluid dynamics modelling and analysis of the effect of 3-D distortion of the human aortic arch. Comput Methods Biomech Biomed Engin. 5:249–260. Mori D, Hayasaka T, Yamaguchi T. 2002b. Modelling of the human aortic arch with its major branches for computational fluid dynamics simulation of the blood flow. JSME. C-45(4):997-1002. Shahcheraghi N, Dwyer HA, Cheer AY, Barakat AI, Rutanganira T. 2002. Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J Biomech Eng. 124(4):378-87. Jin S, Oshinski J, Giddens DP. 2003. Effect of wall motion and compliance on flow patterns in the ascending aorta. J. Biomech. Eng. 125:347–354. Leuprecht A, Kozerke S, Boesiger P, Perktold K. 2003. Blood flow in the human ascending aorta: a combined MRI and CFD study. Journal of Engineering Mathematics. 47:387–404. Kim T, Cheer AY, Dwyer HA. 2004. A simulated dye method for flow visualization with a computational model for blood flow. J Biomech. 27:1125–1136. Morris L, Delassus P, Callanan A, Walsh M, Wallis F, Grace P, McGloughlin T. 2005. 3-D numerical simulation of blood flow through models of the human aorta. J Biomech Eng. 127:767-775. Gao F, Watanabe M, Matsuzawa T. 2006. Stress analysis in a layered aortic arch model under pulsatile blood flow. Biomed. Eng Online. 5:25. Gao F, Matsuzawa T. 2006. FSI within aortic arch model over cardiac cycle and Influence of wall stiffness on wall stress in layered wall. Engineering Letters. 13:167-172. Gao F, Guo Z, Sakamoto M, Matsuzawa T. 2006. Fluid structure interaction within a layered aortic arch model. Journal of Biological Physics. 32(5):435–454. Gardhagen R, Renner J, Lanne T, Karlsson M. 2006. Subject specific wall shear stress in the human thoracic aorta. WSEAS Transaction on Biology and Biomedicine. 3(10):609-614. Park YJ, Park CY, Hwang CM, Sun K, Min BG. 2007. Pseudo-organ boundary conditions applied to a computational fluid dynamics model of the human aorta. Comput. Biol. Med. 37(8):1063-1072. Gao F, Ohta O, Matsuzawa T. 2008. Fluid-structure interaction in layered aortic arch aneurysm model: assessing the combined influence of arch aneurysm and wall stiffness. Australas Phys Eng Sci Med. 3(1):32-41. Lam SK, Fung GSK, Cheng SWK, Chow WK. 2008. A computational study on the biomechanical factors related to stent-graft models in the thoracic aorta. Med Biol Eng Comput. 46:1129–1138. Soulis JV, Giannoglou GD, Dimitrakopoulou M, Logothetides S, Mikhailidis D. 2009. Influence of oscillating flow on LDL transport and wall shear stress in the normal aortic arch. Open Cardiovasc Med J. 17:128-142. Renner J, Gardhagen R, Heiberg E, Ebbers T, Loyd D, Länne T, Karlsson M. 2009. A method for subject specific estimation of aortic wall shear stress. WSEAS Transaction on Biology and Biomedicine. 6(3):49-57. Renner J, Loyd D, Lanne T, Karlsson M. 2009. Is a flat inlet profile sufficient for WSS estimation in the aortic arch? WSEAS Transactions on Fluid Mechanics. 4(4):148-160. Kim HJ, Vignon-Clementel IE, Figueroa CA, LaDisa JF Jr, Jansen KE, Feinstein JA, Taylor CA. 2009. On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Ann Biomed Eng. 37(11):2153–2169. Liu X, Pu F, Fan Y. 2009. A numerical study on the flow of blood and the transport of LDL in the human aorta: the physiological significance of the helical flow in the aortic arch. Am J Physiol Heart Circ Physiol. 297: H163-H170. Tan FPP, Torii R, Borghi A, Mohiaddin RH, Wood NB, Thom S, Xu XY. 2009. Analysis of flow patterns in a patient-specific thoracic aortic aneurysm model. Computers and Structures. 87:680-690. Wen CY, Yang AS, Tseng LY, Chai JW. 2010. Investigation of pulsatile flow field in healthy thoracic aorta models. Ann Biomed Eng. 38(2):391-402. Liu X, Fan YB, Deng XY. 2010. Effect of spiral flow on the transport of oxygen in the aorta: A numerical study. Ann Biomed Eng. 38:917-926. Wang X, Li X. 2011. Biomechanical behaviors of curved artery with flexible wall: a numerical study using fluid-structure interaction method. Comput Biol Med. 41(11):1014-1021. Wang X, Li X. 2011. Computational simulation of aortic aneurysm using FSI method: influence of blood viscosity on aneurismal dynamic behaviors. Comput Biol Med. 41(9):812-821. Liu X, Fan Y, Deng X, Zhan F. 2011. Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta. J Biomech. 44(6):1123-1131. Crosetto P, Reymond P, Deparis S; Kontaxakis D, Stergiopulos N, Quarteroni A. 2011. Fluid-structure interaction simulation of aortic blood flow. Computers & Fluids. 43:46-57. Soulis JV, Fytanidis DK, Papaioannou VC, Styliadis H Giannoglou GD. 2011. Oscillating LDL accumulation in normal human aortic arch - shear dependent endothelium. Hippokratia. 15:22–25. Benim AC, Nahavandi A, Assmann A, Schubert D, Feindt P, Suh SH. 2011. Simulation of blood flow in human aorta with emphasis on outlet boundary conditions. Appl Math Modell. 35(7):3175-3188. Lantz J, Renner J, Karlsson M. 2011. Wall shear stress in a subject specific human aorta - Influence of fluid-structure interaction. Int. J. Appl. Mechanics. 3:759-778. Tse KM, Chiu P, Lee HP, Ho P. 2011. Investigation of hemodynamics in the development of dissecting aneurysm within patient-specific dissecting aneurismal aortas using computational fluid dynamics (CFD) simulations. J Biomech. 44(5):827-836. Filipovic N, Milasinovic D, Zdravkovic N, Böckler D, von Tengg-Kobligk H. 2011. Impact of aortic repair based on flow field computer simulation within the thoracic aorta. Comput Methods Programs Biomed. 101(3): 243-252. Keshavarz-Motamed Z, Kadem L. 2011. 3D pulsatile flow in a curved tube with coexisting model of aortic stenosis and coarctation of the aorta. Med Eng Phys. 33(3):315-324. Olivieri LJ, de Zélicourt DA, Haggerty CM, Ratnayaka K, Cross RR, Yoganathan AP. 2011. Hemodynamic modelling of surgically repaired coarctation of the aorta. Cardiovasc Eng Technol. 2(4):288-295. LaDisa JF Jr, Figueroa CA, Vignon-Clementel IE, Kim HJ, Xiao N, Ellwein LM, Chan FP, Feinstein JA, Taylor CA. 2011a. Computational simulations for aortic coarctation: representative results from a sampling of patients. J Biomech Eng. 133(9):81-89. LaDisa JF Jr, Dholakia RJ, Figueroa CA, Vignon-Clementel IE, Chan FP, Samyn MM, Cava JR, Taylor CA, Feinstein JA. 2011b. Computational simulations demonstrate altered wall shear stress in aortic coarctation patients treated by resection with end-to-end anastomosis. Congenit Heart Dis. 6(5):432-443. Gallo D, De Santis G, Negri F, Tresoldi D, Ponzini R, Massai D, Deriu MA, Segers P, Verhegghe B, Rizzo G, Morbiducci U. 2012. On the use of in vivo measured flow rates as boundary conditions for image-based hemodynamic models of the human aorta: implications for indicators of abnormal flow. Ann Biomed Eng. 40(3):729-41. Lantz J, Karlsson M. 2012. Large eddy simulation of LDL surface concentration in a subject specific human aorta. J Biomech. 45(3):537-542. Lantz J, Gardhagen R, Karlsson M. 2012. Quantifying turbulent wall shear stress in a subject specific human aorta using large eddy simulation. Med Eng Phys. 34(8):1139-1148. Brown AG, Shi Y, Marzo A, Staicu C, Valverde I, Beerbaum P, Lawford PV, Hose DR. 2012. Accuracy vs. computational time: translating aortic simulations to the clinic. J Biomech. 45(3):516-523. Vasava P, Jalali P, Dabagh M, Kolari P. 2012. Finite element modelling of pulsatile blood flow in idealized model of human aortic arch: Study of hypotension and hypertension. Comp. Math. Methods in Medicine. doi: 10.1155/2012/861837. Moireau P, Xiao N, Astorino M, Figueroa CA, Chapelle D, Taylor CA, Gerbeau JF. 2012a. External tissue support and fluid- structure simulation in blood flows. Biomech Model Mechanobiol. 11:1–18. Reymond P, Crosetto P, Deparis S, Quarteroni A, Stergiopulos N. 2012. Physiological simulation of blood flow in the aorta: Comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models. Med Eng Phys. http://dx.doi.org/10.1016/j.medengphy.2012.08.009. Coogan JS, Humphrey JD, Figueroa CA. 2012b. Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodelling in response to distal aortic coarctation. Biomech Model Mechanobiol. doi: 10.1007/s10237-012-0383-x. Coogan JS, Chan FP, LaDisa JF Jr, Taylor CA, Hanley FL, Feinstein JA. 2012a. Computational fluid dynamic simulations for determination of ventricular workload in aortic arch obstructions. J Thorac Cardiovasc Surg. doi: 10.1016/j.jtcvs.2012.03.051. Wendell DC, Samyn MM, Cava JR, Ellwein LM, Krolikowski MM, Gandy KL, Pelech AN, Shadden SC, LaDisa JF Jr. 2012. Including aortic valve morphology in computational fluid dynamics simulations: Initial findings and application to aortic coarctation. Med Eng Phys. http://dx.doi.org/10.1016/j.medengphy.2012.07.015. Morbiducci U, Ponzini R, Gallo D, Bignardi C, Rizzo G. 2013. Inflow boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta. J Biomech. 46:102-109. Cardiovascular diseases (CVDs), Fact sheet 317. In: World Health Organization. 2012. http://www.who.int/mediacentre/factsheets/fs317/en/index.html. Accessed 15 December 2012 Davies PF, Mundel T, Barbee KA. 1995. A mechanism for heterogeneous endotelial responses to flow in vivo and in vitro. Journal of Biomechanics. 28:1553-1560. Davies PF, Dewey CF, Bussolari S, Gordon E, Gimbrone MA. 1984. Influence of hemodynamic forces on vascular endothelial function. In vitro studies of shear stress and pinocytosis in bovine aortic cells. Journal of Clinical Investigation. 73:1121-1129. Gimbrone Jr MA, Topper JN, Nagel T, Anderson KR, Garcia-Cardena G. 2000. Endothelial dysfunction, hemodynamic forces, and atherogenesis. Ann N Y Acad Sci. 902:230–239. Resnick N, Yahav H, Shay-Salit A, Shushy M, Schubert S, Zilberman LC, Wofovitz E. 2003. Fluid shear stress and the vascular endothelium: for better and for worse. Prog Biophys Mol Biol. 81(3):177–199. White CR, Frangos JA. 2007. The shear stress of it all: the cell membrane and mechanochemical transduction. Phil Trans R Soc B. 362:1459–1467. Ku DN, Giddens DP, Zarins CK, Glagov S. 1985. Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis. 5(3):293–302. Moore J, Xu C, Glagov S, Zarins CK, Ku DN. 1994. Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis. 110(2):225–240. Cheng C, Tempel D, van Haperen R, van der Baan A, Grosveld F, Daemen MJ, Krams R, de Crom R. 2006. Atherosclerotic lesion size and vulnerability are determined by patterns of fluid shear stress. Circulation. 113(23):2744–2753. Cecchi E, Giglioli C, Valente S, Lazzeri C, Gensini GF, Abbate R, Mannini L. 2011. Role of hemodynamic shear stress in cardiovascular disease. Atherosclerosis. 214(2):249-256. Friedman MH, Deters OJ, Mark FF, Bargeron CB, Hutchins GM. 1983. Arterial geometry affects hemodynamics. A potential risk factor for athersoclerosis. Arteriosclerosis. 46(2):225-231. Ku DN. 1997. Blood flow in arteries. Annu Rev Fluid Mech. 29:399-434. Cunningham KS, Gotlieb AI. 2005. The role of shear stress in the pathogenesis of atherosclerosis. Lab Invest. 85(1):9–23. Wahle A, Lopez JJ, Olszewski ME, Vigmostad SC, Chandran KB, Rossen JD, Sonka M. 2006. Plaque development, vessel curvature, and wall shear stress in coronary arteries assessed by X-ray angiography and intravascular ultrasound. Med Image Anal. 10(4):615-631. |
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Laín Beatove, Santiagovirtual::2568-1Caballero Gaviria, Andrés Davida7feb95f8865a2beeedb06362515b965Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2020-01-16T14:58:41Z2020-01-16T14:58:41Z2013-06Caballero, A.D., & Laín, S. (2013). A Review on Computational Fluid Dynamics Modelling in Human Thoracic Aorta. Cardiovascular Engineering and Technology, 4, 103-130. DOI: 10.1007/s13239-013-0146-6http://red.uao.edu.co//handle/10614/1180610.1007/s13239-013-0146-6It has long been recognized that the forces and stresses produced by the blood flow on the walls of the cardiovascular system are central to the development of different cardiovascular diseases. However, up to now, the reason why arterial diseases occur at preferential sites is still not fully understood. This paper reviews the progress, made largely within the last decade, towards the use of 3D computational fluid dynamics (CFD) models to simulate the blood flow dynamics and its interaction with the arterial wall within the human thoracic aorta (TA). We describe the technical aspects of model building, review methods to create anatomic and physiologic models, obtain material properties, assign boundary conditions, solve the equations governing blood flow , and describe the assumptions used in running the simulations. Detailed comparative information is provided in tabular format about the model setup, simulation results, and a summary of the major insights and contributions of each TA article reviewed. Several syntheses are given that summarize the research carried out by influential research groups, review important findings, discuss the methods employed, limitations, and opportunities for further research. We hope that this review will stimulate computational research that will contribute to the continued improvement of cardiovascular health through a strong interaction and cooperation between engineers and cliniciansapplication/pdf44 páginasengUniversidad Autónoma de OccidenteCardiovascular Engineering and Technology. páginas 1-3213021034Cardiovascular Engineering and TechnologyMori D, Yamaguchi T. 2002a. Computational fluid dynamics modelling and analysis of the effect of 3-D distortion of the human aortic arch. Comput Methods Biomech Biomed Engin. 5:249–260.Mori D, Hayasaka T, Yamaguchi T. 2002b. Modelling of the human aortic arch with its major branches for computational fluid dynamics simulation of the blood flow. JSME. C-45(4):997-1002.Shahcheraghi N, Dwyer HA, Cheer AY, Barakat AI, Rutanganira T. 2002. Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J Biomech Eng. 124(4):378-87.Jin S, Oshinski J, Giddens DP. 2003. Effect of wall motion and compliance on flow patterns in the ascending aorta. J. Biomech. Eng. 125:347–354.Leuprecht A, Kozerke S, Boesiger P, Perktold K. 2003. Blood flow in the human ascending aorta: a combined MRI and CFD study. Journal of Engineering Mathematics. 47:387–404.Kim T, Cheer AY, Dwyer HA. 2004. A simulated dye method for flow visualization with a computational model for blood flow. J Biomech. 27:1125–1136.Morris L, Delassus P, Callanan A, Walsh M, Wallis F, Grace P, McGloughlin T. 2005. 3-D numerical simulation of blood flow through models of the human aorta. J Biomech Eng. 127:767-775.Gao F, Watanabe M, Matsuzawa T. 2006. Stress analysis in a layered aortic arch model under pulsatile blood flow. Biomed. Eng Online. 5:25.Gao F, Matsuzawa T. 2006. FSI within aortic arch model over cardiac cycle and Influence of wall stiffness on wall stress in layered wall. Engineering Letters. 13:167-172.Gao F, Guo Z, Sakamoto M, Matsuzawa T. 2006. Fluid structure interaction within a layered aortic arch model. Journal of Biological Physics. 32(5):435–454.Gardhagen R, Renner J, Lanne T, Karlsson M. 2006. Subject specific wall shear stress in the human thoracic aorta. WSEAS Transaction on Biology and Biomedicine. 3(10):609-614.Park YJ, Park CY, Hwang CM, Sun K, Min BG. 2007. Pseudo-organ boundary conditions applied to a computational fluid dynamics model of the human aorta. Comput. Biol. Med. 37(8):1063-1072.Gao F, Ohta O, Matsuzawa T. 2008. Fluid-structure interaction in layered aortic arch aneurysm model: assessing the combined influence of arch aneurysm and wall stiffness. Australas Phys Eng Sci Med. 3(1):32-41.Lam SK, Fung GSK, Cheng SWK, Chow WK. 2008. A computational study on the biomechanical factors related to stent-graft models in the thoracic aorta. Med Biol Eng Comput. 46:1129–1138.Soulis JV, Giannoglou GD, Dimitrakopoulou M, Logothetides S, Mikhailidis D. 2009. Influence of oscillating flow on LDL transport and wall shear stress in the normal aortic arch. Open Cardiovasc Med J. 17:128-142.Renner J, Gardhagen R, Heiberg E, Ebbers T, Loyd D, Länne T, Karlsson M. 2009. A method for subject specific estimation of aortic wall shear stress. WSEAS Transaction on Biology and Biomedicine. 6(3):49-57.Renner J, Loyd D, Lanne T, Karlsson M. 2009. Is a flat inlet profile sufficient for WSS estimation in the aortic arch? WSEAS Transactions on Fluid Mechanics. 4(4):148-160.Kim HJ, Vignon-Clementel IE, Figueroa CA, LaDisa JF Jr, Jansen KE, Feinstein JA, Taylor CA. 2009. On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Ann Biomed Eng. 37(11):2153–2169.Liu X, Pu F, Fan Y. 2009. A numerical study on the flow of blood and the transport of LDL in the human aorta: the physiological significance of the helical flow in the aortic arch. Am J Physiol Heart Circ Physiol. 297: H163-H170.Tan FPP, Torii R, Borghi A, Mohiaddin RH, Wood NB, Thom S, Xu XY. 2009. Analysis of flow patterns in a patient-specific thoracic aortic aneurysm model. Computers and Structures. 87:680-690.Wen CY, Yang AS, Tseng LY, Chai JW. 2010. Investigation of pulsatile flow field in healthy thoracic aorta models. Ann Biomed Eng. 38(2):391-402.Liu X, Fan YB, Deng XY. 2010. Effect of spiral flow on the transport of oxygen in the aorta: A numerical study. Ann Biomed Eng. 38:917-926.Wang X, Li X. 2011. Biomechanical behaviors of curved artery with flexible wall: a numerical study using fluid-structure interaction method. Comput Biol Med. 41(11):1014-1021.Wang X, Li X. 2011. Computational simulation of aortic aneurysm using FSI method: influence of blood viscosity on aneurismal dynamic behaviors. Comput Biol Med. 41(9):812-821.Liu X, Fan Y, Deng X, Zhan F. 2011. Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta. 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