Simulation of unsteady blood flow dynamics in the thoracic aorta

En este trabajo se analiza la dinámica del flujo sanguíneo en un modelo realista de la aorta torácica (TA, por sus siglas en inglés) en condiciones transitorias visualizando las distribuciones de velocidad, flujo secundario, presión y esfuerzos cortantes parietales (WSS). Los resultados obtenidos mu...

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Autores:: Laín Beatove, Santiago
Caballero Gaviria, Andrés David

Tipo de recurso:: Article of journal

Fecha de publicación:: 2017

Institución:: Universidad Autónoma de Occidente

Repositorio:: RED: Repositorio Educativo Digital UAO

Idioma:: eng

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dc.title.eng.fl_str_mv	Simulation of unsteady blood flow dynamics in the thoracic aorta
dc.title.alternative.spa.fl_str_mv	Simulación transitoria de la dinámica del flujo sanguíneo en la aorta torácica
title	Simulation of unsteady blood flow dynamics in the thoracic aorta
spellingShingle	Simulation of unsteady blood flow dynamics in the thoracic aorta Simulación por computadores Computer simulation Esfuerzos cortantes parietales Aorta torácica Hemodinámica Thoracic aorta Dinámica de fluidos computacional Flujo sanguíneo Wall shear stress Hemodynamics Computational fluid dynamics Blood flow
title_short	Simulation of unsteady blood flow dynamics in the thoracic aorta
title_full	Simulation of unsteady blood flow dynamics in the thoracic aorta
title_fullStr	Simulation of unsteady blood flow dynamics in the thoracic aorta
title_full_unstemmed	Simulation of unsteady blood flow dynamics in the thoracic aorta
title_sort	Simulation of unsteady blood flow dynamics in the 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.armarc.spa.fl_str_mv	Simulación por computadores
topic	Simulación por computadores Computer simulation Esfuerzos cortantes parietales Aorta torácica Hemodinámica Thoracic aorta Dinámica de fluidos computacional Flujo sanguíneo Wall shear stress Hemodynamics Computational fluid dynamics Blood flow
dc.subject.armarc.eng.fl_str_mv	Computer simulation
dc.subject.proposal.spa.fl_str_mv	Esfuerzos cortantes parietales Aorta torácica Hemodinámica Thoracic aorta Dinámica de fluidos computacional Flujo sanguíneo
dc.subject.proposal.eng.fl_str_mv	Wall shear stress Hemodynamics Computational fluid dynamics Blood flow
description	En este trabajo se analiza la dinámica del flujo sanguíneo en un modelo realista de la aorta torácica (TA, por sus siglas en inglés) en condiciones transitorias visualizando las distribuciones de velocidad, flujo secundario, presión y esfuerzos cortantes parietales (WSS). Los resultados obtenidos muestran que la velocidad primaria del flujo tiende hacia la pared interior de la aorta ascendente, pero esta, a su vez, tiende hacia la pared posterior en el arco aórtico y hacia las paredes anterior y exterior en la aorta descendente. En las tres ramificaciones del arco aórtico la velocidad del flujo se acerca hacia las paredes distales mostrando recirculación del flujo en las cercanías de las paredes proximales. En la TA se observa un flujo secundario intenso, especialmente a la entrada de las ramificaciones del arco. Finalmente, la presión es baja a lo largo de la pared interior de la aorta y en las paredes proximales de las ramificaciones, mientras que es alta en las zonas de estancamiento situadas en las paredes distales de las ramificaciones así como a lo largo de la pared exterior de la aorta ascendente.
publishDate	2017
dc.date.issued.none.fl_str_mv	2017
dc.date.accessioned.none.fl_str_mv	2019-10-21T19:24:40Z
dc.date.available.none.fl_str_mv	2019-10-21T19:24:40Z
dc.type.spa.fl_str_mv	Artículo de revista
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dc.relation.cites.spa.fl_str_mv	Laín, S., y Caballero, A. D. (2017). Simulation of unsteady blood flow dynamics in the thoracic aorta. Ingeniería e Investigación, 37(3), 92-101
dc.relation.ispartofjournal.spa.fl_str_mv	Ingeniería e Investigación
dc.relation.references.none.fl_str_mv	Caballero, AD., Laín, S. (2013). A Review on Computational Fluid Dynamics Modelling in Human Thoracic Aorta. Cardiovascular Engineering and Technology, 4, 103-130. Caballero, AD., Laín, S. (2015). Numerical Simulation of non-Newtonian Blood Flow Dynamics in Human Thoracic Aorta. Computer Methods in Biomechanics and Biomedical Engineering, 18, 1200-1216. Cecchi, E., Giglioli, C., Valente, S., Lazzeri, C., Gensini, G.F., Abbate, R., Mannini, L. (2011). Role of hemodynamic shear stress in cardiovascular disease. Atherosclerosis., 214, 249-256. Chandran, K.B. (1993). Flow Dynamics in the Human Aorta. J Biomech Eng., 115, 611–616. Dabagh, M., Vasava, P., & Jalali, P. (2015). Effects of severity and location of stenosis on the hemodynamics in human aorta and its branches. Medical & biological engineering & computing, 53(5), 463-476. Fung, Y.C. (1997). Biomechanics Circulation. 2nd ed. Springer. Gallo, D., Gülan, U., Di Stefano, A., Ponzini, R., Lüthi, B., Holzner, M., & Morbiducci, U. (2014). Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics. Journal of biomechanics, 47(12), 3149-3155. Kern, M.J., Lim, M.J., Goldstein, J.A. (2009). Hemodynamic Rounds: Interpretation of Cardiac Pathophysiology from Pressure Waveform Analysis Transport Phenomena in the Cardiovascular System. 3rd ed. Wiley-Blackwell. Kilner, P.J., Yang, G.Z., Mohiaddin, R.H., Firmin, D.N., Longmore, D.B. (1993). Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping., Circulation. 88(5), 2235-2247. 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), 123-1131. Liepsch, D., Moravec, S.T., Baumgart, R. (1992). Some flow visualization and laser-Doppler velocity measurements in a tube-to-scale elastic model of a human arotic arch—a new model technique. Biorheology., 29, 563–580. 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, 1139-1148. Middleman, S. (1972). Transport Phenomena in the Cardiovascular System. 1st ed. John Wiley and Sons. Morbiducci, U., Ponzini, R., Rizzo, G., Cadioli, M., Esposito, A., Montevecchi, F.M., Redaelli, A. (2011). Mechanistic insight into the physiological relevance of helical blood flow in the human aorta. An in vivo study. Biomech Model Mechanobiol, 10, 339–355. 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. 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. Mori, D., & Yamaguchi, T. (2002). Computational fluid dynamics modeling and analysis of the effect of 3-D distortion of the human aortic arch. Computer Methods in Biomechanics & Biomedical Engineering, 5(3), 249-260. Nerem, R.M., Rumberger, J.A., Gross, D.R., Hamlin, R.L., Geiger, G.L. (1974). Hot-Film Anemometry Velocity Measurements of Arterial Blood Flow in Horses. CircRes, 10, 301–313. Park, Y.J., Park, C.Y., Hwang, C.M., Sun, K., Min, B.G., (2007). Pseudo-organ boundary conditions applied to a computational fluid dynamics model of the human aorta. Comput. Biol., Med. 37, (8), 1063-1072. Pedley, T.J. (1980). The Fluid Mechanics of Large Blood Vessels. Cambridge University Press, Cambridge. Prakash, S., Ethier, C.R. (2001). Requirements for mesh resolution in 3D computational hemodynamics. J. Biomech Eng., 23, 134–144. Seed, W.A., Wood, N.B. (1971). Velocity Patterns in the Aorta. Cardiovasc, Res. 5, 319–330. Shahcheraghi, N., Dwyer, H.A., Cheer, A.Y., Barakat, AI., Rutanganira, T. (2002). Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J. Biomech Eng., 124, 378-87. Simbios project, (2007). Retrieved from: https://simtk.org/xml/index.xml, http://simbios.stanford.edu/ 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., 2012, Article ID 861837. Versteeg. H.K., Malalasekera, W. (2007). An introduction to computational fluid dynamics. The finite volume method. Pearson, London. Wen, C.Y., Yang, A.S., Tseng, L.Y.,Chai, JW. (2010). Investigation of Pulsatile flow field in healthy thoracic aorta models. Ann Biomed Eng., 38, 391-402. White, F. M. (1979). Viscous Fluid Flow, McGraw-Hill, New York. Womersley, J.R. (1955). Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure is known. J Physiol., 127, 553–563.
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spelling	Laín Beatove, Santiagovirtual::2543-1Caballero Gaviria, Andrés Davida7feb95f8865a2beeedb06362515b965Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-10-21T19:24:40Z2019-10-21T19:24:40Z201722488723 (en línea)01205609 (impresa)http://hdl.handle.net/10614/11243https://doi.org/10.15446/ing.investig.v37n3.59761En este trabajo se analiza la dinámica del flujo sanguíneo en un modelo realista de la aorta torácica (TA, por sus siglas en inglés) en condiciones transitorias visualizando las distribuciones de velocidad, flujo secundario, presión y esfuerzos cortantes parietales (WSS). Los resultados obtenidos muestran que la velocidad primaria del flujo tiende hacia la pared interior de la aorta ascendente, pero esta, a su vez, tiende hacia la pared posterior en el arco aórtico y hacia las paredes anterior y exterior en la aorta descendente. En las tres ramificaciones del arco aórtico la velocidad del flujo se acerca hacia las paredes distales mostrando recirculación del flujo en las cercanías de las paredes proximales. En la TA se observa un flujo secundario intenso, especialmente a la entrada de las ramificaciones del arco. Finalmente, la presión es baja a lo largo de la pared interior de la aorta y en las paredes proximales de las ramificaciones, mientras que es alta en las zonas de estancamiento situadas en las paredes distales de las ramificaciones así como a lo largo de la pared exterior de la aorta ascendente.In this work, blood flow dynamics was analyzed in a realistic thoracic aorta (TA) model under unsteady-state conditions via velocity contours, secondary flow, pressure and wall shear stress (WSS) distributions. Our results demonstrated that the primary flow velocity is skewed towards the inner wall of the ascending aorta; but this skewness shifts towards the posterior wall in the aortic arch and then towards the anterior-outer wall in the descending aorta. Within the three arch branches, the flow velocity is skewed to the distal walls with flow reversal along the proximal walls. Strong secondary flow motion is observed in the TA, especially at the inlet of the arch branches. WSS is highly dynamic, but was found to be the lowest along the proximal walls of the arch branches. Finally, pressure was found to be low along the inner aortic wall and in the proximal walls of the arch branches, and high around the three stagnation regions distal to the arch branches and along the outer wall of the ascending aortaapplication/pdf10 páginasengUniversidad Nacional de Colombia. Facultad de IngenieríaDerechos Reservados - Universidad Autónoma de Occidentehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Simulation of unsteady blood flow dynamics in the thoracic aortaSimulación transitoria de la dinámica del flujo sanguíneo en la aorta torácicaArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Simulación por computadoresComputer simulationEsfuerzos cortantes parietalesAorta torácicaHemodinámicaThoracic aortaDinámica de fluidos computacionalFlujo sanguíneoWall shear stressHemodynamicsComputational fluid dynamicsBlood flow10139237Laín, S., y Caballero, A. D. (2017). Simulation of unsteady blood flow dynamics in the thoracic aorta. Ingeniería e Investigación, 37(3), 92-101Ingeniería e InvestigaciónCaballero, AD., Laín, S. (2013). A Review on Computational Fluid Dynamics Modelling in Human Thoracic Aorta. Cardiovascular Engineering and Technology, 4, 103-130.Caballero, AD., Laín, S. (2015). Numerical Simulation of non-Newtonian Blood Flow Dynamics in Human Thoracic Aorta. Computer Methods in Biomechanics and Biomedical Engineering, 18, 1200-1216.Cecchi, E., Giglioli, C., Valente, S., Lazzeri, C., Gensini, G.F., Abbate, R., Mannini, L. (2011). Role of hemodynamic shear stress in cardiovascular disease. Atherosclerosis., 214, 249-256.Chandran, K.B. (1993). Flow Dynamics in the Human Aorta. J Biomech Eng., 115, 611–616.Dabagh, M., Vasava, P., & Jalali, P. (2015). Effects of severity and location of stenosis on the hemodynamics in human aorta and its branches. Medical & biological engineering & computing, 53(5), 463-476.Fung, Y.C. (1997). Biomechanics Circulation. 2nd ed. Springer.Gallo, D., Gülan, U., Di Stefano, A., Ponzini, R., Lüthi, B., Holzner, M., & Morbiducci, U. (2014). Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics. Journal of biomechanics, 47(12), 3149-3155.Kern, M.J., Lim, M.J., Goldstein, J.A. (2009). Hemodynamic Rounds: Interpretation of Cardiac Pathophysiology from Pressure Waveform Analysis Transport Phenomena in the Cardiovascular System. 3rd ed. Wiley-Blackwell.Kilner, P.J., Yang, G.Z., Mohiaddin, R.H., Firmin, D.N., Longmore, D.B. (1993). Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping., Circulation. 88(5), 2235-2247.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), 123-1131.Liepsch, D., Moravec, S.T., Baumgart, R. (1992). Some flow visualization and laser-Doppler velocity measurements in a tube-to-scale elastic model of a human arotic arch—a new model technique. Biorheology., 29, 563–580.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, 1139-1148.Middleman, S. (1972). Transport Phenomena in the Cardiovascular System. 1st ed. John Wiley and Sons.Morbiducci, U., Ponzini, R., Rizzo, G., Cadioli, M., Esposito, A., Montevecchi, F.M., Redaelli, A. (2011). Mechanistic insight into the physiological relevance of helical blood flow in the human aorta. An in vivo study. Biomech Model Mechanobiol, 10, 339–355.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.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.Mori, D., & Yamaguchi, T. (2002). Computational fluid dynamics modeling and analysis of the effect of 3-D distortion of the human aortic arch. Computer Methods in Biomechanics & Biomedical Engineering, 5(3), 249-260.Nerem, R.M., Rumberger, J.A., Gross, D.R., Hamlin, R.L., Geiger, G.L. (1974). Hot-Film Anemometry Velocity Measurements of Arterial Blood Flow in Horses. CircRes, 10, 301–313.Park, Y.J., Park, C.Y., Hwang, C.M., Sun, K., Min, B.G., (2007). Pseudo-organ boundary conditions applied to a computational fluid dynamics model of the human aorta. Comput. Biol., Med. 37, (8), 1063-1072.Pedley, T.J. (1980). The Fluid Mechanics of Large Blood Vessels. Cambridge University Press, Cambridge.Prakash, S., Ethier, C.R. (2001). Requirements for mesh resolution in 3D computational hemodynamics. J. Biomech Eng., 23, 134–144.Seed, W.A., Wood, N.B. (1971). Velocity Patterns in the Aorta. Cardiovasc, Res. 5, 319–330.Shahcheraghi, N., Dwyer, H.A., Cheer, A.Y., Barakat, AI., Rutanganira, T. (2002). Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J.Biomech Eng., 124, 378-87.Simbios project, (2007). Retrieved from: https://simtk.org/xml/index.xml, http://simbios.stanford.edu/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., 2012, Article ID 861837.Versteeg. H.K., Malalasekera, W. (2007). An introduction to computational fluid dynamics. The finite volume method. Pearson, London.Wen, C.Y., Yang, A.S., Tseng, L.Y.,Chai, JW. (2010). Investigation of Pulsatile flow field in healthy thoracic aorta models. Ann Biomed Eng., 38, 391-402.White, F. M. (1979). Viscous Fluid Flow, McGraw-Hill, New York.Womersley, J.R. (1955). Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure is known. J Physiol., 127, 553–563.Publication082b0926-3385-4188-9c6a-bbbed7484a95virtual::2543-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::2543-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::2543-10000-0002-0269-2608virtual::2543-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::2543-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/7edd8d41-bf93-4d91-a000-9a053ab08642/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/fc05fec1-0161-4d85-925d-66a842c4d4e3/download20b5ba22b1117f71589c7318baa2c560MD53ORIGINALSimulation of unsteady blood flow dynamics in the thoracic aorta.pdfSimulation of unsteady blood flow dynamics in the thoracic aorta.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf1372780https://red.uao.edu.co/bitstreams/0a70c026-a238-42fd-9143-91d0abd442f1/download29950bf69a9585926dd758d06ce945ddMD54TEXTSimulation of unsteady blood flow dynamics in the thoracic aorta.pdf.txtSimulation of unsteady blood flow dynamics in the thoracic aorta.pdf.txtExtracted texttext/plain38983https://red.uao.edu.co/bitstreams/2b4febb7-e13e-463a-a9db-062719576e3d/download52807e4918aadb5f49d56fbee0c5f398MD55THUMBNAILSimulation of unsteady blood flow dynamics in the thoracic aorta.pdf.jpgSimulation of unsteady blood flow dynamics in the thoracic aorta.pdf.jpgGenerated Thumbnailimage/jpeg15218https://red.uao.edu.co/bitstreams/f60ef906-8f74-48e7-9330-832e2c1f61b5/downloadbe2c82ecac9cf36fc1a403e42f9ef1a5MD5610614/11243oai:red.uao.edu.co:10614/112432024-03-06 16:16:07.216https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidenteopen.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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

Simulation of unsteady blood flow dynamics in the thoracic aorta

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