A three-layer model for buckling of a human aortic segment under specific flow-pressure conditions

International Journal for Numerical Methods in Biomedical Engineering

Volumn 28, Issue 5, 2012, Pages 495-512

  Amabili, M ^a   Karazis, K ^a   Mongrain, R ^a,b   Paidoussis M P ^a   Cartier, R ^b  

^a MCGILL UNIVERSITY   (Canada)

^b MONTREAL HEART INSTITUTE   (Canada)

Author keywords

Bifurcation analysis; Buckling; Human aorta; Nonlinear continuation analysis; Nonlinear laminated shell model; Reduced order model

Indexed keywords

BIFURCATION ANALYSIS; CONTINUATION ANALYSIS; HUMAN AORTA; LAMINATED SHELL; REDUCED ORDER MODELS;

BIFURCATION (MATHEMATICS); BUCKLING; DEFORMATION; HEMODYNAMICS; LAMINATED COMPOSITES; MODEL STRUCTURES; NAVIER STOKES EQUATIONS; PRESSURIZATION; STRESSES; TISSUE;

BLOOD VESSELS;

AORTA; ARTERIAL STIFFNESS; BIOLOGICAL MODEL; BIOMECHANICS; HUMAN; NONLINEAR SYSTEM; PATHOPHYSIOLOGY; PHYSIOLOGY; PRESSURE;

AORTA; BIOMECHANICAL PHENOMENA; HUMANS; MODELS, CARDIOVASCULAR; NONLINEAR DYNAMICS; PRESSURE; VASCULAR STIFFNESS;

EID: 84860459581     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1484     Document Type: Article

References (74)

1. Bertram CD. The dynamics of collapsible tubes. 1995.
2. Kamm RD, Pedley TJ. Flow in collapsible tubes: A brief review. Journal of Biomechanical Engineering 1989; 111:177-179.
3. Païdoussis MP. Fluid-Structure Interactions: Slender Structures and Axial Flow. Vol. 2, Elsevier Academic Press: London, UK, 2004.
4. Heil M. The stability of cylindrical shells conveying viscous flow. Journal of Fluids and Structures 1996; 10:173-196.
5. Heil M. Stokes flow in collapsible tubes - Computation and experiment. Journal of Fluid Mechanics 1998; 353:285-312.
6. Luo XY, Pedley TJ. Flow and instability in collapsible tubes. ZAMM Zeitschrift für Angewandte Mathematik und Mechanik 1996; 76:37-40.
7. Pedley TJ, Luo XY. Modelling flow and oscillations in collapsible tubes. Theoretical and Computational Fluid Dynamics 1998; 10:277-294.
8. Barabas M, Gosselin G, Crépeau J, Petitclerc R, Cartier R, Théroux P. Left main stenting-as a bridge to surgery- for acute type A aortic dissection and anterior myocardial infarction. Catheterization and Cardiovascular Intervention 2000; 51:74-77.
9. Fuster V, Halperin JL. Aortic dissection: A medical perspective. Journal of Cardiac Surgery 1994; 9:713-728.
10. Roberts WC. Aortic dissection: Anatomy, consequences, and causes. American Heart Journal 1981; 101:195-214.
11. Khanafer K, Berguer R. Fluid-structure interaction analysis of turbulent pulsatile flow within a layered aortic wall as related to aortic dissection. Journal of Biomechanics 2009; 42:2642-2648.
12. Xavier R, Bourdeaud'hui A, Collet D, Laborde N, Baudet E. Traumatic rupture and aneurysm of the aortic isthmus: Late results of repair by direct suture. Annals of Vascular Surgery 1989; 3:47-51.
13. Chavanon O, Carrier M, Cartier R, Hébert Y, Pellerin M, Pagé P, Perrault LP. Increased incidence of acute ascending aortic dissection with off-pump aortocoronary bypass surgery. Annals of Thoracic Surgery 2001; 71:117-121.
14. Wang DS, Dake MD. Endovascular therapy for aortic dissection. In Thoracic Aortic Diseases. Rousseau H, Verhoye JP, Heautot JF (eds). Springer: New York, NY, 2006; 189-198.
15. Gao F, Watanabe M, Matsuazawa T. Stress analysis in a layered aortic arch model under pulsatile blood flow. BioMedical Engineering Online 2006a; 5:25.
16. Gao F, Guo Z, Sakamoto M, Matsuzawa T. Fluid-structure interaction within a layered aortic arch model. Journal of Biological Physics 2006b; 32:435-454.
17. Pemberton J, Sahn DJ. Imaging of the aorta. International Journal of Cardiology 2004; 97:53-60.
18. Kalita P, Schaefer R. Mechanical models of artery walls. Archives of Computational Methods in Engineering 2008; 15:1-36.
19. Balzani D. Simulation of deformation, damage and residual stresses in arterial walls. Advanced Engineering Materials 2008; 10:315-321.
20. Holzapfel GA. Determination of material models for arterial walls from uniaxial extension tests and histological structure. Journal of Theoretical Biology 2006; 238:290-302.
21. Brum J, Balay G, Bia D, Benech N, Ramos A, Armantano R, Negreira C. Improvement of Young modulus examination by ultrasound using static pressure steps. Physics Procedia 2010; 3:1087-1094.
22. Choudury N, Bouchot O, Rouleau L, Tremblay D, Cartier R, Mongrain R, Leask RL. Local mechanical and structural poperties of healthy and diseased human ascending aorta tissue. Cardiovascular Pathology 2009; 18:83-91.
23. Holzapfel GA, Sommer G, Regitnig P. Anisotropic mechanical properties of tissue components in human atherosclerotic plaques. Journal of Biomechanical Engineering 2004b; 126:657-665.
24. Holzapfel GA, Sommer G, Gasser CT, Regitnig P. Determination of layer-specifc mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling. American Journal of Physiology - Heart and Circulatory Physiology 2005; 289:H2048-H2058.
25. Iliopoulos DC, Deveja RP, Kritharis EP, Perrea D, Sionis GD, Toutouzas K, Stefanidis C, Sokolis DP. Regional and directional variations in the mechanical properties of ascending thoracic aortic aneurysms. Medical Enginering & Physics 2009; 31:1-9.
26. Loree HM, Grodzinsky AJ, Park SY, Gibson LJ, Lee RT. Static circumferential tangential modulus of human atherosclerotic tissue. Journal of Biomechanics 1994; 27:195-204.
27. Sommer G, Gasser TC, Regitnig P, Auer M, Holzapfel GA. Dissection properties of the human aortic media: An experimental study. Journal of Biomechanical Engineering 2008; 130:0210071-02100712.
28. Teng Z, Tang D, Zheng J, Woodard PK, Hoffman AH. An experimental study on the ultimate strength of the adventitia and media of human atherosclerotic carotid arteries in circumferential and axial directions. Journal of Biomechanics 2009; 42:2535-2539.
29. Tremblay D, Zigras T, Cartier R, Leduc L, Butany J, Mongrain R, Leask RL. A comparison of mechanical properties of materials used in aortic arch reconstruction. The Annals of Thoracic Surgery 2009; 88:1484-1491.
30. Holzapfel GA, Ogden RW. Constitutive modelling of arteries. Proceedings of the Royal Society A 2010a; 466:1551-1597.
31. Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity 2000; 61:1-48.
32. Holzapfel G, Gasser TC, Ogden RW. Comparison of a multi-layer structural model for arterial walls with a Fung-type model, and issues of material stability. Journal of Biomechanical Engineering 2004a; 126:264-275.
33. Holzapfel GA, Ogden RW. Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta. Journal of the Royal Society Interface 2010b; 7:787-799.
34. Rodríguez JF, Ruiz C, Doblaré M, Holzapfel GA. Mechanical stresses in abdominal aortic aneurysms: Influence of diameter, asymmetry, and material anisotropy. Journal of Biomechanical Engineering 2008; 130:0210231-02102310.
35. Goriely A, Vandiver R. On the mechanical stability of growing arteries. IMA Journal of Applied Mathematics 2010; 75:549-570.
36. Holzapfel GA, Sommer G, Auer M, Regitnig P, Ogden RW. Layer-specific 3D residual deformations of human aortas with non-atherosclerotic intimal thickening. Annals in Biomedical Engineering 2007; 35:530-545.
37. Taylor CA, Humphrey JD. Open problems in computational vascular biomechanics: Hemodynamics and arterial wall mechanics. Computational Methods in Applied Mechanics and Engineering 2009; 198:3514-3523.
38. Frydrychowicz A, Stalder AF, Russe MF, Bock J, Bauer S, Harloff A, Berger A, Langer M, Hennig J, Markl M. Three-dimensional analysis of segmental wall shear stress in the aorta by flow-sensitive four-dimensional MRI. Journal of Magnetic Resonance Imaging 2009; 30:77-84.
39. Wen C-Y, Yang A-S, Tseng L-Y, Chai J-W. Investigation of pulsatile flowfield in healthy thoracic aorta models. Annals of Biomedical Engineering 2010; 38:391-402.
40. Heil M, Pedley TJ. Large post-buckling deformations of cylindrical shells conveying viscous flow. Journal of Fluids and Structures 1996; 10:565-599.
41. Amabili M, Pellicano F, Païdoussis MP. Nonlinear dynamics and stability of circular cylindrical shells containing flowing fluid. Part I: Stability. Journal of Sound and Vibration 1999; 225:655-699.
42. Karagiozis KN, Païdoussis MP, Amabili M, Misra AK. Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments. Journal of Sound and Vibration 2008; 309:637-676.
43. Amabili M, Karagiozis K, Païdoussis MP. Effect of geometric imperfections on nonlinear stability of circular cylindrical shells conveying fluid. International Journal of Non-Linear Mechanics 2009; 44:276-289.
44. Amabili M. Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press: New York, USA, 2008.
45. Amabili M, Farhadi S. Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates. Journal of Sound and Vibration 2009; 320:649-667.
46. Reddy JN. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition, CRC Press: Boca Raton, FL, USA, 2004.
47. Bluth EI, Murphey SM, Hollier LH, Sullivan MA. Color flow Doppler in the evaluation of aortic aneurysms. International Angiology 1990; 9:8-10.
48. Cheng Z, Tan FPP, Riga CV, Bicknell CD, Hamady MS, Gibbs RGJ, Wood NB, Xu XY. Analysis of flow patterns in a patient-specific aortic dissection model. Journal of Biomechanical Engineering 2010; 132:051007.
49. Egelhoff CJ, Budwig RS, Elger DF, Khraishi TA, Johanses KH. Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions. Journal of Biomechanics 1999; 32:1319-1329.
50. Jozwik K, Obidowski D. Numerical simulations of the blood flow through vertebral arteries. Journal of Biomechanics 2010; 43:177-185.
51. Khanafer KM, Bull JL, Berguer R. Fluid-structure interaction of turbulent pulsatile flow within a flexible wall axisymmetric aortic aneurysm model. European Journal of Mechanics B/Fluids 2009; 28:88-102.
52. Li JK-J. Laminar and turbulent flow in the mammalian aorta: Reynolds number. Journal of Theoretical Biology 1988; 135:409-414.
53. Nerem RM, Seed WA, Wood NB. An experimental study of the velocity distribution and transition to turbulence in the aorta. Journal of Fluid Mechanics 1972; 52:137-160.
54. Paul MC, Molla MMd, Roditi G. Large-Eddy simulation of pulsatile blood flow. Medical Engineering & Physics 2009; 31:153-159.
55. De Langre E, Ouvrard AE. Absolute and convective bending instabilities in fluid-conveying pipes. Journal of Fluids and Structures 1999; 13:663-680.
56. Païdoussis MP, Denise J-P. Flutter of thin shells conveying fluid. Journal of Sound and Vibration 1972; 20:9-26.
57. Païdoussis MP, Misra AK, Chan SP. Dynamics and stability of coaxial cylindrical shells conveying viscous fluid. Journal of Applied Mechanics 1985; 52:389-396.
58. Doedel EJ, Champneys AR, Fairgrieve TF, Kuznetsov YA, Sandstede B, Wang X. AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont). Concordia University: Montreal, Canada, 1998.
59. Thubrikar MJ, Agali P, Robicsek F. Wall stress as a possible mechanism for the development of transverse intimal tears in aortic dissections. Journal of Medical Engineering & Technology 1999; 23:127-134.
60. Ranga A, Mongrain R, Mendes Galaz R, Biadillah Y, Cartier R. Large-displacement 3D structural analysis of an aortic valve model with nonlinear material properties. Journal of Medical Engineering and Technology 2004; 28:95-103.
61. Johnston BM, Johnston PR, Corney S, Kilpatrick D. Non-Newtonian blood flow in human right coronary arteries: steady state simulations. Journal of Biomechanics 2004; 37:709-720.
62. Farcas MA, Rouleau L, Fraser R, Leask RL. The development of 3-D, in vitro, endothelial culture models for the study of coronary artery disease. Biomedical Engineering Online 2009; 8:30.
63. Liu SQ, Yen M, Fung YC. On measuring the third dimension of cultured endothelial cells in shear flow. Proceedings of the National Academy of the United States of America 1994; 91:8782-8786.
64. Mills C, Gabe I, Gault J, Mason D, Ross J, Braumwald E, Shillingford J. Pressure-flow relationships and vascular impedance in man. Cardiovascular Research 1970; 4:405-417.
65. Labrosse MR, Beller CJ, Mesana T, Veinot JP. Mechanical behavior of human aortas: Experiments, material constants and 3-D finite element modeling including residual stress. Journal of Biomechanics 2009; 42:996-1004.
66. Conrad MF, Crawford RS, Kwolek CJ, Brewster DC, Brady TJ, Cambria RP. Aortic remodeling after endovascular repair of acute complicated type B aortic dissection. Journal of Vascular Surgery 2009; 50:510-517.
67. Rowland TW, Grarrard M, Marwood S, Guerra ME, Roce D, Unnithan VB. Myocardial performance during progressive exercise in athletic adolescent males. Medicine & Science in Sports & Exercise 2009; 41:1721-1728.
68. Novelline RA, Rhea JT, Rao PM, Stuk JL. Helical CT in emergency radiology. Radiology 1999; 213:321-339.
69. Takeda S, Rimington H, Chambers J. Prediction of symptom-onset in aortic stenosis: a comparison of pressure drop/flow slope and haemodynamic measures at rest. International Journal of Cardiology 2001; 81:131-137.
70. Karagiozis KN, Païdoussis MP, Amabili M. Effect of geometry on the stability of cylindrical clamped shells subjected to internal fluid flow. Computers & Structures 2007; 85:645-659.
71. De Putter S, Wolters BJBM, Rutten MCM, Breeuwer M, Gerritsen FA, van de Vosse FN. Patient-specific initial wall stress in abdominal aortic aneurysms with a backward incremental method. Journal of Biomechanics 2007; 40:1081-1090.
72. Raghavan ML, Vorp DA. Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. Journal of Biomechanics 2000; 33:475-482.
73. Johnston BM, Johnston PR, Corney S, Kilpatrick D. Non-Newtonian blood flow in human right coronary arteries: Transient simulations. Journal of Biomechanics 2006; 39:1116-1128.
74. Volokh KY, Vorp DA. A model of growth and rupture of abdominal aortic aneurysm. Journal of Biomechanics 2008; 41:1015-1021.