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February  2017, 14(1): 179-193. doi: 10.3934/mbe.2017012

Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery

1. 

Dept. Math., IST, Univ. Lisboa and CEMAT, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

2. 

Dept. of CS. and Math., LAU, P-36, Byblos, Lebanon

* Corresponding author: oualid.kafi@tecnico.ulisboa.pt

Received  December 2015 Accepted  May 04, 2016 Published  October 2016

Fund Project: The first author is supported by PHYSIOMATH project EXCL/MAT-NAN/0114/2012

The inflammatory process of atherosclerosis leads to the formation of an atheromatous plaque in the intima of the blood vessel. The plaque rupture may result from the interaction between the blood and the plaque. In each cardiac cycle, blood interacts with the vessel, considered as a compliant nonlinear hyperelastic. A three dimensional idealized fluid-structure interaction (FSI) model is constructed to perform the blood-plaque and blood-vessel wall interaction studies. An absorbing boundary condition (BC) is imposed directly on the outflow in order to cope with the spurious reflexions due to the truncation of the computational domain. The difference between the Newtonian and non-Newtonian effects is highlighted. It is shown that the von Mises and wall shear stresses are significantly affected according to the rigidity of the wall. The numerical results have shown that the risk of plaque rupture is higher in the case of a moving wall, while in the case of a fixed wall the risk of progression of the atheromatous plaque is higher.

Citation: Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179-193. doi: 10.3934/mbe.2017012
References:
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B. S. AribisalaZ. MorrisE. EadieA. ThomasA. GowM. C. Valdés HernándezN. A. RoyleM. E. BastinJ. StarrI. J. Deary and J. M. Wardlaw, Blood pressure, internal carotid artery flow parameters and age-related white matter hyperintensities, Hypertension, 63 (2014), 1011-1018. doi: 10.1161/HYPERTENSIONAHA.113.02735. Google Scholar

[2]

S. BoujenaO. Kafi and N. El Khatib, A 2D mathematical model of blood flow and its interactions in the atherosclerotic artery, Math Model Nat Phenom, 9 (2014), 46-68. doi: 10.1051/mmnp/20149605. Google Scholar

[3]

S. BoujenaO. Kafi and N. El Khatib, Generalized Navier-Stokes equations with non-standard conditions for blood flow in atherosclerotic artery, Appl Anal, 95 (2016), 1645-1670. doi: 10.1080/00036811.2015.1068297. Google Scholar

[4]

Y. C. ChangT. Y. HouB. Merriman and S. Osher, A level set formulation of eulerian interface capturing methods for incompressible fluid flows, J Comput Phys, 124 (1996), 449-464. doi: 10.1006/jcph.1996.0072. Google Scholar

[5]

P. G. Ciarlet, Mathematical Elasticity. Vol. 1, Three Dimensional Elasticity, Elsevier, 2004.Google Scholar

[6]

M. CillaE. Peña and M. A. Martínez, 3D computational parametric analysis of eccentric atheroma plaque: Influence of axial and circumferential residual stresses, Biomech Model Mechanobiol, 11 (2012), 1001-1013. doi: 10.1007/s10237-011-0369-0. Google Scholar

[7]

COMSOL Multiphysics, User's Guide 4. 3b, Licence 17073661,2012.Google Scholar

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P. CrosettoP. RaymondS. DeparisD. KontaxakisN. Stergiopulos and A. Quarteroni, Fluid-structure interaction simulations of physiological blood flow in the aorta, Comput Fluids, 43 (2011), 46-57. doi: 10.1016/j.compfluid.2010.11.032. Google Scholar

[9]

J. DoneaS. Giuliani and J. P. Halleux, An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions, Comput Methods Appl Mech Engrg, 33 (1982), 689-723. doi: 10.1016/0045-7825(82)90128-1. Google Scholar

[10]

N. El KhatibS. Genieys and V. Volpert, Atherosclerosis initiation modeled as an inflammatory process, Math Model Nat Phenom, 2 (2007), 126-141. doi: 10.1051/mmnp:2008022. Google Scholar

[11]

J. Fan and T. Watanabe, Inflammatory reactions in the pathogenesis of atherosclerosis, J Atheroscler Thromb, 10 (2003), 63-71. doi: 10.5551/jat.10.63. Google Scholar

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L. FormaggiaA. Moura and F. Nobile, On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations, ESAIM-Math Model Num, 41 (2007), 743-769. doi: 10.1051/m2an:2007039. Google Scholar

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L. Formaggia and A. Veneziani, Reduced and multiscale models for the human cardiovascular system. Lecture Notes, VKI Lecture Series, 2013.Google Scholar

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S. Frei, T. Richter and T. Wick, Eulerian techniques for fluid-structure interactions -part Ⅱ: Applications. In A. Abdulle, S. Deparis, D. Kressner, F. Nobile and M. Picasso editors, Numerical Mathematics and Advanced Applications, ENUMATH 2013, Springer (2015), 745-754. doi: 10.1016/0045-7825(82)90128-1. Google Scholar

[15]

A. M. GambarutoJ. JanelaA. Moura and A. Sequeira, Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology, Math Biosci Eng, 8 (2011), 409-423. doi: 10.3934/mbe.2011.8.409. Google Scholar

[16]

S. GlagovE. WeisenbergC. K. ZarinsR. Stankunavicius and G. J. Kolettis, Compensatory enlargement of human atherosclerotic coronary arteries, N Engl J Med, 316 (1987), 1371-1375. doi: 10.1056/NEJM198705283162204. Google Scholar

[17]

R. GlowinskiT. W. Pan and J. Periaux, A fictitious domain method for Dirichlet problem and applications, Comput Method Appl M, 111 (1994), 283-303. doi: 10.1016/0045-7825(94)90135-X. Google Scholar

[18]

R. GlowinskiT. W. Pan and J. Periaux, A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 112 (1994), 133-148. doi: 10.1016/0045-7825(94)90022-1. Google Scholar

[19]

T. GuerraA. Sequeira and J. Tiago, Optimal control in blood flow simulations, Int J Nonlinear Mech, 64 (2014), 57-69. doi: 10.1016/j.ijnonlinmec.2014.04.005. Google Scholar

[20]

W. HaoA. Friedman and J. Tiago, The LDL-HDL profile determines the risk of atherosclerosis: A mathematical model, A Mathematical Model. PLoS ONE, 9 (2014), e90497. doi: 10.1371/journal.pone.0090497. Google Scholar

[21]

T. J. R. HughesW. K. Liu and T. K. Zimmermann, Arbitrary lagrangian-eulerian finite element formulation for incompressible viscous flows, Comput Method Appl M, 29 (1981), 329-349. doi: 10.1016/0045-7825(81)90049-9. Google Scholar

[22]

I. HusainF. LabropuluC. Langdon and J. Schwark, A comparison of Newtonian and non-Newtonian models for pulsatile blood flow simulations, J Mech Behav Mater, 21 (2013), 147-153. Google Scholar

[23]

J. JanelaA. Moura and A. Sequeira, A 3D non-Newtonian fluid-structure interaction model for blood flow in arteries, J. Comput. Appl. Math., 234 (2010), 2783-2791. doi: 10.1016/j.cam.2010.01.032. Google Scholar

[24]

J. JanelaA. Moura and A. Sequeira, Absorbing boundary conditions for a 3D non-Newtonian fluid-structure interaction model for blood flow in arteries, Internat. J. Engrg. Sci., 48 (2010), 1332-1349. doi: 10.1016/j.ijengsci.2010.08.004. Google Scholar

[25]

S. A. KockJ. V. NygaardN. EldrupE. T. FründA. KlærkeW. P. PaaskeE. Falk and W. Y. Kim, Mechanical stresses in carotid plaques using MRI-based fluid-structure interaction models, J Biomech, 41 (2008), 1651-1658. doi: 10.1016/j.jbiomech.2008.03.019. Google Scholar

[26]

S. Le Floc'hJ. OhayonP. TracquiG. FinetA. M. GharibR. L. MauriceG. Cloutier and R. I. Pettigrew, Vulnerable atherosclerotic plaque elasticity reconstruction based on a segmentation-driven optimization procedure using strain measurements: theoretical framework, IEEE T Med Imaging, 28 (2009), 1126-1137. doi: 10.1109/TMI.2009.2012852. Google Scholar

[27]

Z. Y. LiS. HowarthT. Tang and J. H. Gillard, How critical is fibrous cap thickness to carotid plaque stability? A flow plaque interaction model, Stroke, 37 (2006), 1195-1199. doi: 10.1161/01.STR.0000217331.61083.3b. Google Scholar

[28]

Z. Y. LiS. HowarthR. A. TrivediJ. M. U-King-ImM. J. GravesA. BrownL. Wang and J. H. Gillard, Stress analysis of carotid plaque rupture based on in vivo high resolution MRI, J Biomech, 39 (2006), 2611-2622. doi: 10.1016/j.jbiomech.2005.08.022. Google Scholar

[29]

B. Muha and S. Čanić, Existence of a solution to a fluid-multi-layered-structure interaction problem, J Differ Equations, 256 (2014), 658-706. doi: 10.1016/j.jde.2013.09.016. Google Scholar

[30]

F. Nobile, Numerical Approximation of Fluid-Structure Interaction Problems with Application to Haemodynamics, Ph. D thesis, École Polytechnique Fédérale de Lausanne, Switzerland, 2001.Google Scholar

[31]

C. S. Peskin, Numerical analysis of blood flow in the heart, J Comput Phys, 25 (1977), 220-252. doi: 10.1016/0021-9991(77)90100-0. Google Scholar

[32]

C. S. Peskin and D. M. McQueen, A three-dimensional computational method for blood flow in the heart -Ⅰ Immersed elastic fibers in a viscous incompressible fluid, J Comput Phys, 81 (1989), 372-405. doi: 10.1016/0021-9991(89)90213-1. Google Scholar

[33]

R. N. Poston and D. R. M. Poston, A typical atherosclerotic plaque morphology produced in silico by an atherogenesis model based on self-perpetuating propagating macrophage recruitment, Math Model Nat Phenom, 2 (2007), 142-149. doi: 10.1051/mmnp:2008030. Google Scholar

[34]

A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system. in computational models for the human body, Ciarlet PG (eds). Handbook of Numerical Analysis, North-Holland: Amsterdam, 12 (2004), 3-127. Google Scholar

[35]

T. Quillard and P. Libby, Molecular imaging of atherosclerosis for improving diagnostic and therapeutic development, Circ Res, 111 (2012), 231-244. doi: 10.1161/CIRCRESAHA.112.268144. Google Scholar

[36]

S. RamalhoA. MouraA. M. Gambaruto and A. Sequeira, Sensitivity to outflow boundary conditions and level of geometry description for a cerebral aneurysm, Int J Numer Method Biomed Eng, 28 (2012), 697-713. doi: 10.1002/cnm.2461. Google Scholar

[37]

R. Ross, Atherosclerosis -An inflammatory disease, Massachusetts Medical Society, 340 (1999), 115-120. Google Scholar

[38]

G. Ruiz-AresB. FuentesP. Martínez-Sanchéz and E. Díez-Tejedor, A prediction model for unstable carotid atheromatous plaque in acute ischemic stroke patients: proposal and internal validation, Ultrasound in Med. & Biol., 40 (2014), 1958-1965. doi: 10.1016/j.ultrasmedbio.2014.04.015. Google Scholar

[39]

L. G. SpagnoliE. BonannoG. Sangiorgi and A. Mauriello, Role of inflammation in atherosclerosis, J Nucl Med, 48 (2007), 1800-1815. doi: 10.2967/jnumed.107.038661. Google Scholar

[40]

D. TangC. YangJ. ZhengP. K. WoodardG. A. SicardJ. E. Saffitz and C. Yuan, 3D MRI-based multicomponent FSI models for atherosclerotic plaques, Ann Biomed Eng, 32 (2004), 947-960. Google Scholar

[41]

T. Wick, Flapping and contact FSI computations with the fluid-solid interface-tracking/ interface-capturing technique and mesh adaptivity, Comput Mech, 53 (2014), 29-43. doi: 10.1007/s00466-013-0890-3. Google Scholar

[42]

Y. YangW. JägerM. Neuss-Radu and T. Richter, Mathematical modeling and simulation of the evolution of plaques in blood vessels, J Math Biol, 72 (2016), 973-996. doi: 10.1007/s00285-015-0934-8. Google Scholar

[43]

J. YuanZ. TengJ. FengY. ZhangA. J. BrownJ. H. GillardZ. Jing and Q. Lu, Influence of material property variability on the mechanical behaviour of carotid atherosclerotic plaques: A 3D fluid-structure interaction analysis, Int J Numer Method Biomed Eng, 31 (2015), p2722. doi: 10.1002/cnm.2722. Google Scholar

show all references

References:
[1]

B. S. AribisalaZ. MorrisE. EadieA. ThomasA. GowM. C. Valdés HernándezN. A. RoyleM. E. BastinJ. StarrI. J. Deary and J. M. Wardlaw, Blood pressure, internal carotid artery flow parameters and age-related white matter hyperintensities, Hypertension, 63 (2014), 1011-1018. doi: 10.1161/HYPERTENSIONAHA.113.02735. Google Scholar

[2]

S. BoujenaO. Kafi and N. El Khatib, A 2D mathematical model of blood flow and its interactions in the atherosclerotic artery, Math Model Nat Phenom, 9 (2014), 46-68. doi: 10.1051/mmnp/20149605. Google Scholar

[3]

S. BoujenaO. Kafi and N. El Khatib, Generalized Navier-Stokes equations with non-standard conditions for blood flow in atherosclerotic artery, Appl Anal, 95 (2016), 1645-1670. doi: 10.1080/00036811.2015.1068297. Google Scholar

[4]

Y. C. ChangT. Y. HouB. Merriman and S. Osher, A level set formulation of eulerian interface capturing methods for incompressible fluid flows, J Comput Phys, 124 (1996), 449-464. doi: 10.1006/jcph.1996.0072. Google Scholar

[5]

P. G. Ciarlet, Mathematical Elasticity. Vol. 1, Three Dimensional Elasticity, Elsevier, 2004.Google Scholar

[6]

M. CillaE. Peña and M. A. Martínez, 3D computational parametric analysis of eccentric atheroma plaque: Influence of axial and circumferential residual stresses, Biomech Model Mechanobiol, 11 (2012), 1001-1013. doi: 10.1007/s10237-011-0369-0. Google Scholar

[7]

COMSOL Multiphysics, User's Guide 4. 3b, Licence 17073661,2012.Google Scholar

[8]

P. CrosettoP. RaymondS. DeparisD. KontaxakisN. Stergiopulos and A. Quarteroni, Fluid-structure interaction simulations of physiological blood flow in the aorta, Comput Fluids, 43 (2011), 46-57. doi: 10.1016/j.compfluid.2010.11.032. Google Scholar

[9]

J. DoneaS. Giuliani and J. P. Halleux, An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions, Comput Methods Appl Mech Engrg, 33 (1982), 689-723. doi: 10.1016/0045-7825(82)90128-1. Google Scholar

[10]

N. El KhatibS. Genieys and V. Volpert, Atherosclerosis initiation modeled as an inflammatory process, Math Model Nat Phenom, 2 (2007), 126-141. doi: 10.1051/mmnp:2008022. Google Scholar

[11]

J. Fan and T. Watanabe, Inflammatory reactions in the pathogenesis of atherosclerosis, J Atheroscler Thromb, 10 (2003), 63-71. doi: 10.5551/jat.10.63. Google Scholar

[12]

L. FormaggiaA. Moura and F. Nobile, On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations, ESAIM-Math Model Num, 41 (2007), 743-769. doi: 10.1051/m2an:2007039. Google Scholar

[13]

L. Formaggia and A. Veneziani, Reduced and multiscale models for the human cardiovascular system. Lecture Notes, VKI Lecture Series, 2013.Google Scholar

[14]

S. Frei, T. Richter and T. Wick, Eulerian techniques for fluid-structure interactions -part Ⅱ: Applications. In A. Abdulle, S. Deparis, D. Kressner, F. Nobile and M. Picasso editors, Numerical Mathematics and Advanced Applications, ENUMATH 2013, Springer (2015), 745-754. doi: 10.1016/0045-7825(82)90128-1. Google Scholar

[15]

A. M. GambarutoJ. JanelaA. Moura and A. Sequeira, Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology, Math Biosci Eng, 8 (2011), 409-423. doi: 10.3934/mbe.2011.8.409. Google Scholar

[16]

S. GlagovE. WeisenbergC. K. ZarinsR. Stankunavicius and G. J. Kolettis, Compensatory enlargement of human atherosclerotic coronary arteries, N Engl J Med, 316 (1987), 1371-1375. doi: 10.1056/NEJM198705283162204. Google Scholar

[17]

R. GlowinskiT. W. Pan and J. Periaux, A fictitious domain method for Dirichlet problem and applications, Comput Method Appl M, 111 (1994), 283-303. doi: 10.1016/0045-7825(94)90135-X. Google Scholar

[18]

R. GlowinskiT. W. Pan and J. Periaux, A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 112 (1994), 133-148. doi: 10.1016/0045-7825(94)90022-1. Google Scholar

[19]

T. GuerraA. Sequeira and J. Tiago, Optimal control in blood flow simulations, Int J Nonlinear Mech, 64 (2014), 57-69. doi: 10.1016/j.ijnonlinmec.2014.04.005. Google Scholar

[20]

W. HaoA. Friedman and J. Tiago, The LDL-HDL profile determines the risk of atherosclerosis: A mathematical model, A Mathematical Model. PLoS ONE, 9 (2014), e90497. doi: 10.1371/journal.pone.0090497. Google Scholar

[21]

T. J. R. HughesW. K. Liu and T. K. Zimmermann, Arbitrary lagrangian-eulerian finite element formulation for incompressible viscous flows, Comput Method Appl M, 29 (1981), 329-349. doi: 10.1016/0045-7825(81)90049-9. Google Scholar

[22]

I. HusainF. LabropuluC. Langdon and J. Schwark, A comparison of Newtonian and non-Newtonian models for pulsatile blood flow simulations, J Mech Behav Mater, 21 (2013), 147-153. Google Scholar

[23]

J. JanelaA. Moura and A. Sequeira, A 3D non-Newtonian fluid-structure interaction model for blood flow in arteries, J. Comput. Appl. Math., 234 (2010), 2783-2791. doi: 10.1016/j.cam.2010.01.032. Google Scholar

[24]

J. JanelaA. Moura and A. Sequeira, Absorbing boundary conditions for a 3D non-Newtonian fluid-structure interaction model for blood flow in arteries, Internat. J. Engrg. Sci., 48 (2010), 1332-1349. doi: 10.1016/j.ijengsci.2010.08.004. Google Scholar

[25]

S. A. KockJ. V. NygaardN. EldrupE. T. FründA. KlærkeW. P. PaaskeE. Falk and W. Y. Kim, Mechanical stresses in carotid plaques using MRI-based fluid-structure interaction models, J Biomech, 41 (2008), 1651-1658. doi: 10.1016/j.jbiomech.2008.03.019. Google Scholar

[26]

S. Le Floc'hJ. OhayonP. TracquiG. FinetA. M. GharibR. L. MauriceG. Cloutier and R. I. Pettigrew, Vulnerable atherosclerotic plaque elasticity reconstruction based on a segmentation-driven optimization procedure using strain measurements: theoretical framework, IEEE T Med Imaging, 28 (2009), 1126-1137. doi: 10.1109/TMI.2009.2012852. Google Scholar

[27]

Z. Y. LiS. HowarthT. Tang and J. H. Gillard, How critical is fibrous cap thickness to carotid plaque stability? A flow plaque interaction model, Stroke, 37 (2006), 1195-1199. doi: 10.1161/01.STR.0000217331.61083.3b. Google Scholar

[28]

Z. Y. LiS. HowarthR. A. TrivediJ. M. U-King-ImM. J. GravesA. BrownL. Wang and J. H. Gillard, Stress analysis of carotid plaque rupture based on in vivo high resolution MRI, J Biomech, 39 (2006), 2611-2622. doi: 10.1016/j.jbiomech.2005.08.022. Google Scholar

[29]

B. Muha and S. Čanić, Existence of a solution to a fluid-multi-layered-structure interaction problem, J Differ Equations, 256 (2014), 658-706. doi: 10.1016/j.jde.2013.09.016. Google Scholar

[30]

F. Nobile, Numerical Approximation of Fluid-Structure Interaction Problems with Application to Haemodynamics, Ph. D thesis, École Polytechnique Fédérale de Lausanne, Switzerland, 2001.Google Scholar

[31]

C. S. Peskin, Numerical analysis of blood flow in the heart, J Comput Phys, 25 (1977), 220-252. doi: 10.1016/0021-9991(77)90100-0. Google Scholar

[32]

C. S. Peskin and D. M. McQueen, A three-dimensional computational method for blood flow in the heart -Ⅰ Immersed elastic fibers in a viscous incompressible fluid, J Comput Phys, 81 (1989), 372-405. doi: 10.1016/0021-9991(89)90213-1. Google Scholar

[33]

R. N. Poston and D. R. M. Poston, A typical atherosclerotic plaque morphology produced in silico by an atherogenesis model based on self-perpetuating propagating macrophage recruitment, Math Model Nat Phenom, 2 (2007), 142-149. doi: 10.1051/mmnp:2008030. Google Scholar

[34]

A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system. in computational models for the human body, Ciarlet PG (eds). Handbook of Numerical Analysis, North-Holland: Amsterdam, 12 (2004), 3-127. Google Scholar

[35]

T. Quillard and P. Libby, Molecular imaging of atherosclerosis for improving diagnostic and therapeutic development, Circ Res, 111 (2012), 231-244. doi: 10.1161/CIRCRESAHA.112.268144. Google Scholar

[36]

S. RamalhoA. MouraA. M. Gambaruto and A. Sequeira, Sensitivity to outflow boundary conditions and level of geometry description for a cerebral aneurysm, Int J Numer Method Biomed Eng, 28 (2012), 697-713. doi: 10.1002/cnm.2461. Google Scholar

[37]

R. Ross, Atherosclerosis -An inflammatory disease, Massachusetts Medical Society, 340 (1999), 115-120. Google Scholar

[38]

G. Ruiz-AresB. FuentesP. Martínez-Sanchéz and E. Díez-Tejedor, A prediction model for unstable carotid atheromatous plaque in acute ischemic stroke patients: proposal and internal validation, Ultrasound in Med. & Biol., 40 (2014), 1958-1965. doi: 10.1016/j.ultrasmedbio.2014.04.015. Google Scholar

[39]

L. G. SpagnoliE. BonannoG. Sangiorgi and A. Mauriello, Role of inflammation in atherosclerosis, J Nucl Med, 48 (2007), 1800-1815. doi: 10.2967/jnumed.107.038661. Google Scholar

[40]

D. TangC. YangJ. ZhengP. K. WoodardG. A. SicardJ. E. Saffitz and C. Yuan, 3D MRI-based multicomponent FSI models for atherosclerotic plaques, Ann Biomed Eng, 32 (2004), 947-960. Google Scholar

[41]

T. Wick, Flapping and contact FSI computations with the fluid-solid interface-tracking/ interface-capturing technique and mesh adaptivity, Comput Mech, 53 (2014), 29-43. doi: 10.1007/s00466-013-0890-3. Google Scholar

[42]

Y. YangW. JägerM. Neuss-Radu and T. Richter, Mathematical modeling and simulation of the evolution of plaques in blood vessels, J Math Biol, 72 (2016), 973-996. doi: 10.1007/s00285-015-0934-8. Google Scholar

[43]

J. YuanZ. TengJ. FengY. ZhangA. J. BrownJ. H. GillardZ. Jing and Q. Lu, Influence of material property variability on the mechanical behaviour of carotid atherosclerotic plaques: A 3D fluid-structure interaction analysis, Int J Numer Method Biomed Eng, 31 (2015), p2722. doi: 10.1002/cnm.2722. Google Scholar

Figure 1.  3D computational domain of the idealized stenosed artery model composed of fibrous cap, lipid pool and vascular wall
Figure 2.  Inlet pressure waveform.
Figure 3.  Sagittal cut of 3D meshed geometry. The mesh is more refined in the stenosed region (1) and less refined far from the stenosis (parts 2, 3 and 4)
Figure 4.  Extra meshes for convergence study. Detail of regions 1, 2 and 3 (see Figure 3) representing the lumen, fibrous cap and lipid pool. The total number of DOF for the coarse mesh (left) is 359 231 and for the fine mesh (right) is 780 283
Figure 5.  Comparison between the maximal values of WSS in the stenosed region (1) (left) and the total displacement values of the fibrous cap (right) in a coarse, intermediate size and fine mesh
Figure 6.  Total volume displacement of the fibrous cap at the peak of the pressure (t = 0:22 s). The upper figures, left and right, represent the case of a fixed wall where blood is modeled as a New tonian fluid and a shear-thinning non-Newtonian fluid using the Carreau-Yasuda viscosity model, respectively. The representation for the same models in the case of a moving wall is in the lower figures
Figure 7.  Average variation of the WSS at the interface of the volume shown in Figure 6
Figure 9.  The von Mises stress distribution on the fibrous cap at the peak of the pressure (t = 0:22 s). upstream the stenosis for fixed and moving walls (top left and right, respectively) and downstream the stenosis (down left and right, respectively)
Figure 8.  Average variation of the von Mises stress at the inter face of the volume shown in Figure 6
Figure 10.  The WSS distribution on the fibrous cap at the peak of the pressure (t = 0:22 s). upstream the stenosis for fixed and moving walls (top left and right, respectively) and downstream the stenosis (down left and right, respectively)
Figure 11.  Average variation of the WSS at the interface of the volume shown in Figure 6
Table 1.  Parameters used for the plaque components
Plaque components C10 (N.m-2) C01 (N.m-2) κ (MPa) Density (kg.m-3)
Fibrous cap 9200 0 3000 1000
Lipid pool 500 0 200 1000
Plaque components C10 (N.m-2) C01 (N.m-2) κ (MPa) Density (kg.m-3)
Fibrous cap 9200 0 3000 1000
Lipid pool 500 0 200 1000
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