Three Dimensional Large Eddy Simulation of Blood Flow and Deformation in an Elastic Constricted Artery
In the current work, a three-dimensional geometry of a
75% stenosed blood vessel is analyzed. Large eddy simulation (LES)
with the help of a dynamic subgrid scale Smagorinsky model is
applied to model the turbulent pulsatile flow. The geometry, the
transmural pressure and the properties of the blood and the elastic
boundary were based on clinical measurement data. For the flexible
wall model, a thin solid region is constructed around the 75%
stenosed blood vessel. The deformation of this solid region was
modelled as a deforming boundary to reduce the computational cost
of the solid model. Fluid-structure interaction is realized via a twoway
coupling between the blood flow modelled via LES and the
deforming vessel. The information of the flow pressure and the wall
motion was exchanged continually during the cycle by an arbitrary
Lagrangian-Eulerian method. The boundary condition of current time
step depended on previous solutions. The fluctuation of the velocity
in the post-stenotic region was analyzed in the study. The axial
velocity at normalized position Z=0.5 shows a negative value near
the vessel wall. The displacement of the elastic boundary was
concerned in this study. In particular, the wall displacement at the
systole and the diastole were compared. The negative displacement at
the stenosis indicates a collapse at the maximum velocity and the
deceleration phase.
[1] Khader AS, Shenoy SB, Pai RB, Mahmood N, Kamath G, Rao V: A
comparative Fluid-Structure Interaction study of stenosed and normal
Common Carotid Artery. World Journal of Modelling and Simulation
2009, 5(4):272-277.
[2] Ojha M, Cobbold RS, Johnston KW, Hummel RL: Pulsatile flow
through constricted tubes: an experimental investigation using
photochromic tracer methods. Journal of Fluid Mechanics 1989,
203:173-197.
[3] Kajiya F, Tsujioka K, Ogasawara Y, Wada Y, Matsuoka S, Kanazawa S,
Hiramatsu O, Tadaoka S, Goto M, Fujiwara T: Analysis of flow
characteristics in poststenotic regions of the human coronary artery
during bypass graft surgery. Circulation 1987, 76(5):1092-1100.
[4] Jung H, Choi JW, Park CG: Asymmetric flows of non-Newtonian fluids
in symmetric stenosed artery. Korea-Australia Rheology Journal 2004,
16(2):101-108.
[5] Lee K, Xu X: Modelling of flow and wall behaviour in a mildly stenosed
tube. Medical engineering & physics 2002, 24(9):575-586.
[6] Ponalagusamy R: Blood flow through an artery with mild stenosis: A
Two-Layered Model, Different Shapes of Stenoses and Slip Velocity at
the Wall. Journal of Applied Sciences 2007, 7(7):1071-1077.
[7] Pope SB: Turbulent flows: Cambridge university press; 2000.
[8] Paul MC, Mamun Molla M, Roditi G: Large–Eddy simulation of
pulsatile blood flow. Medical engineering & physics 2009, 31(1):153-
159.
[9] Mittal R, Simmons S, Najjar F: Numerical study of pulsatile flow in a
constricted channel. Journal of Fluid Mechanics 2003, 485:337-378.
[10] Mittal R, Simmons S, Udaykumar H: Application of large-eddy
simulation to the study of pulsatile flow in a modeled arterial stenosis.
Journal of biomechanical engineering 2001, 123(4):325-332.
[11] Scotti A, Piomelli U: Turbulence models in pulsating flows. AIAA
journal 2002, 40(3):537-544.
[12] Liang C, Papadakis G: Large eddy simulation of pulsating flow over a
circular cylinder at subcritical Reynolds number. Computers & fluids
2007, 36(2):299-312.
[13] Tan F, Wood N, Tabor G, Xu X: Comparison of LES of steady
transitional flow in an idealized stenosed axisymmetric artery model
with a RANS transitional model. Journal of biomechanical engineering
2011, 133(5):051001.
[14] Fung Y-C: Biomechanics: Springer; 1990.
[15] Holzapfel GA, Weizsäcker HW: Biomechanical behavior of the arterial
wall and its numerical characterization. Computers in biology and
medicine 1998, 28(4):377-392.
[16] Cheng GC, Loree HM, Kamm RD, Fishbein MC, Lee RT: Distribution
of circumferential stress in ruptured and stable atherosclerotic lesions. A
structural analysis with histopathological correlation. Circulation 1993,
87(4):1179-1187.
[17] Lee RT, Loree HM, Cheng GC, Lieberman EH, Jaramillo N, Schoen FJ:
Computational structural analysis based on intravascular ultrasound
imaging before in vitro angioplasty: prediction of plaque fracture
locations. Journal of the American College of Cardiology 1993,
21(3):777-782.
[18] Loree HM, Grodzinsky AJ, Park SY, Gibson LJ, Lee RT: Static
circumferential tangential modulus of human atherosclerotic tissue.
Journal of biomechanics 1994, 27(2):195-204.
[19] Richardson PD, Davies M, Born G: Influence of plaque configuration
and stress distribution on fissuring of coronary atherosclerotic plaques.
The Lancet 1989, 334(8669):941-944.
[20] Zhao S, Xu X, Collins M: The numerical analysis of fluid-solid
interactions for blood flow in arterial structures Part 2: development of
coupled fluid-solid algorithms. Proceedings of the Institution of
Mechanical Engineers, Part H: Journal of Engineering in Medicine 1998,
212(4):241-252.
[21] Chan W, Ding Y, Tu J: Modeling of non-Newtonian blood flow through
a stenosed artery incorporating fluid-structure interaction. ANZIAM
Journal 2007, 47:C507--C523.
[22] Oscuii HN, Shadpour MT, Ghalichi F: Flow Characteristics in Elastic
Arteries Using a Fluid-Structure Interaction Model. American Journal of
Applied Sciences 2007, 4(8):516.
[23] Tang D, Yang C, Kobayashi S, Ku DN: Generalized finite difference
method for 3-D viscous flow in stenotic tubes with large wall
deformation and collapse. Applied numerical mathematics 2001,
38(1):49-68.
[24] McCord BN, Ku DN: Mechanical rupture of the atherosclerotic plaque
fibrous cap. ASME-PUBLICATIONS-BED 1993, 24:324-324.
[25] Chakravarty S, Mandal PK: Two-dimensional blood flow through
tapered arteries under stenotic conditions. International Journal of Non-
Linear Mechanics 2000, 35(5):779-793.
[26] Mandal PK: An unsteady analysis of non-Newtonian blood flow through
tapered arteries with a stenosis. International Journal of Non-Linear
Mechanics 2005, 40(1):151-164.
[27] Hall JE: Guyton and Hall Textbook of Medical Physiology: Enhanced
E-book: Elsevier Health Sciences; 2010.
[28] Black J, Hastings G: Handbook of biomaterial properties: Springer;
1998.
[29] Fluent A: 12.0 UDF Manual. Ansys Inc 2009
[1] Khader AS, Shenoy SB, Pai RB, Mahmood N, Kamath G, Rao V: A
comparative Fluid-Structure Interaction study of stenosed and normal
Common Carotid Artery. World Journal of Modelling and Simulation
2009, 5(4):272-277.
[2] Ojha M, Cobbold RS, Johnston KW, Hummel RL: Pulsatile flow
through constricted tubes: an experimental investigation using
photochromic tracer methods. Journal of Fluid Mechanics 1989,
203:173-197.
[3] Kajiya F, Tsujioka K, Ogasawara Y, Wada Y, Matsuoka S, Kanazawa S,
Hiramatsu O, Tadaoka S, Goto M, Fujiwara T: Analysis of flow
characteristics in poststenotic regions of the human coronary artery
during bypass graft surgery. Circulation 1987, 76(5):1092-1100.
[4] Jung H, Choi JW, Park CG: Asymmetric flows of non-Newtonian fluids
in symmetric stenosed artery. Korea-Australia Rheology Journal 2004,
16(2):101-108.
[5] Lee K, Xu X: Modelling of flow and wall behaviour in a mildly stenosed
tube. Medical engineering & physics 2002, 24(9):575-586.
[6] Ponalagusamy R: Blood flow through an artery with mild stenosis: A
Two-Layered Model, Different Shapes of Stenoses and Slip Velocity at
the Wall. Journal of Applied Sciences 2007, 7(7):1071-1077.
[7] Pope SB: Turbulent flows: Cambridge university press; 2000.
[8] Paul MC, Mamun Molla M, Roditi G: Large–Eddy simulation of
pulsatile blood flow. Medical engineering & physics 2009, 31(1):153-
159.
[9] Mittal R, Simmons S, Najjar F: Numerical study of pulsatile flow in a
constricted channel. Journal of Fluid Mechanics 2003, 485:337-378.
[10] Mittal R, Simmons S, Udaykumar H: Application of large-eddy
simulation to the study of pulsatile flow in a modeled arterial stenosis.
Journal of biomechanical engineering 2001, 123(4):325-332.
[11] Scotti A, Piomelli U: Turbulence models in pulsating flows. AIAA
journal 2002, 40(3):537-544.
[12] Liang C, Papadakis G: Large eddy simulation of pulsating flow over a
circular cylinder at subcritical Reynolds number. Computers & fluids
2007, 36(2):299-312.
[13] Tan F, Wood N, Tabor G, Xu X: Comparison of LES of steady
transitional flow in an idealized stenosed axisymmetric artery model
with a RANS transitional model. Journal of biomechanical engineering
2011, 133(5):051001.
[14] Fung Y-C: Biomechanics: Springer; 1990.
[15] Holzapfel GA, Weizsäcker HW: Biomechanical behavior of the arterial
wall and its numerical characterization. Computers in biology and
medicine 1998, 28(4):377-392.
[16] Cheng GC, Loree HM, Kamm RD, Fishbein MC, Lee RT: Distribution
of circumferential stress in ruptured and stable atherosclerotic lesions. A
structural analysis with histopathological correlation. Circulation 1993,
87(4):1179-1187.
[17] Lee RT, Loree HM, Cheng GC, Lieberman EH, Jaramillo N, Schoen FJ:
Computational structural analysis based on intravascular ultrasound
imaging before in vitro angioplasty: prediction of plaque fracture
locations. Journal of the American College of Cardiology 1993,
21(3):777-782.
[18] Loree HM, Grodzinsky AJ, Park SY, Gibson LJ, Lee RT: Static
circumferential tangential modulus of human atherosclerotic tissue.
Journal of biomechanics 1994, 27(2):195-204.
[19] Richardson PD, Davies M, Born G: Influence of plaque configuration
and stress distribution on fissuring of coronary atherosclerotic plaques.
The Lancet 1989, 334(8669):941-944.
[20] Zhao S, Xu X, Collins M: The numerical analysis of fluid-solid
interactions for blood flow in arterial structures Part 2: development of
coupled fluid-solid algorithms. Proceedings of the Institution of
Mechanical Engineers, Part H: Journal of Engineering in Medicine 1998,
212(4):241-252.
[21] Chan W, Ding Y, Tu J: Modeling of non-Newtonian blood flow through
a stenosed artery incorporating fluid-structure interaction. ANZIAM
Journal 2007, 47:C507--C523.
[22] Oscuii HN, Shadpour MT, Ghalichi F: Flow Characteristics in Elastic
Arteries Using a Fluid-Structure Interaction Model. American Journal of
Applied Sciences 2007, 4(8):516.
[23] Tang D, Yang C, Kobayashi S, Ku DN: Generalized finite difference
method for 3-D viscous flow in stenotic tubes with large wall
deformation and collapse. Applied numerical mathematics 2001,
38(1):49-68.
[24] McCord BN, Ku DN: Mechanical rupture of the atherosclerotic plaque
fibrous cap. ASME-PUBLICATIONS-BED 1993, 24:324-324.
[25] Chakravarty S, Mandal PK: Two-dimensional blood flow through
tapered arteries under stenotic conditions. International Journal of Non-
Linear Mechanics 2000, 35(5):779-793.
[26] Mandal PK: An unsteady analysis of non-Newtonian blood flow through
tapered arteries with a stenosis. International Journal of Non-Linear
Mechanics 2005, 40(1):151-164.
[27] Hall JE: Guyton and Hall Textbook of Medical Physiology: Enhanced
E-book: Elsevier Health Sciences; 2010.
[28] Black J, Hastings G: Handbook of biomaterial properties: Springer;
1998.
[29] Fluent A: 12.0 UDF Manual. Ansys Inc 2009
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:69720", author = "Xi Gu and Guan Heng Yeoh and Victoria Timchenko", title = "Three Dimensional Large Eddy Simulation of Blood Flow and Deformation in an Elastic Constricted Artery", abstract = "In the current work, a three-dimensional geometry of a
75% stenosed blood vessel is analyzed. Large eddy simulation (LES)
with the help of a dynamic subgrid scale Smagorinsky model is
applied to model the turbulent pulsatile flow. The geometry, the
transmural pressure and the properties of the blood and the elastic
boundary were based on clinical measurement data. For the flexible
wall model, a thin solid region is constructed around the 75%
stenosed blood vessel. The deformation of this solid region was
modelled as a deforming boundary to reduce the computational cost
of the solid model. Fluid-structure interaction is realized via a twoway
coupling between the blood flow modelled via LES and the
deforming vessel. The information of the flow pressure and the wall
motion was exchanged continually during the cycle by an arbitrary
Lagrangian-Eulerian method. The boundary condition of current time
step depended on previous solutions. The fluctuation of the velocity
in the post-stenotic region was analyzed in the study. The axial
velocity at normalized position Z=0.5 shows a negative value near
the vessel wall. The displacement of the elastic boundary was
concerned in this study. In particular, the wall displacement at the
systole and the diastole were compared. The negative displacement at
the stenosis indicates a collapse at the maximum velocity and the
deceleration phase.
", keywords = "Large Eddy Simulation, Fluid Structural Interaction,
Constricted Artery, Computational Fluid Dynamics.", volume = "9", number = "5", pages = "731-6", }
