Skip to main content
SpringerLink
Log in

Multi-Scale Modelling of Vascular Disease: Abdominal Aortic Aneurysm Evolution

  • Chapter
  • First Online:
Computational Modeling in Tissue Engineering

Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 10))

Abstract

We present a fluid-solid-growth (FSG) computational framework to simulate the mechanobiology of the arterial wall. The model utilises a realistic constitutive model that accounts for the structural arrangement of collagen fibres in the medial and adventitial layers, the natural reference configurations in which the collagen fibres are recruited to load bearing and the (normalised) mass-density of the elastinous and collagenous constituents. Growth and remodelling (G&R) of constituents is explicitly linked to mechanical stimuli: computational fluid dynamic analysis produces snapshots of the frictional forces acting on the endothelial cells; a quasi-static structural analysis is employed to quantify the cyclic deformation of the vascular cells. We apply the computational framework to simulate the evolution of a specific vascular pathology: abdominal aortic aneurysm (AAA). Two illustrative models of AAA evolution are presented. Firstly, the degradation of elastin (that is observed to accompany AAA evolution) is prescribed, and secondly, it is linked to low levels of wall shear stress (WSS). In the first example, we predict the development of tortuosity that accompanies AAA enlargement, whilst in the latter, we illustrate that linking elastin degradation to low WSS leads to enlarging fusiform AAAs. We conclude that this computational framework provides the basis for further investigating and elucidating the aetiology of AAA and other vascular diseases. Moreover, it has immediate application to tissue engineering, e.g., aiding the design and optimisation of tissue engineered vascular constructs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Barron, V., Lyons, E., Stenson-Cox, C., McHugh, P.E., Pandit, A.: Bioreactors for cardiovascular cell and tissue growth: a review. Ann. Biomed. Eng. 31, 1017–1030 (2003)

    Article  Google Scholar 

  2. Geris, L.: In vivo, in vitro, in silico: computational tools for product and process design in tissue engineering. Springer, Heidelberg (2012)

    Google Scholar 

  3. Vorp, D.A.: Review: Biomechanics of abdominal aortic aneurysm. J. Biomech. 40, 1887–1902 (2007)

    Article  Google Scholar 

  4. Sakalihasan, N., Kuivaniemi, H., Nusgens, B., Durieux, R., Defraigne, J.G.: Aneurysm: epidemiology aetiology and pathophysiology, biomechanics and mechanobiology of aneurysms. Springer, Heidelberg (2011)

    Google Scholar 

  5. Baxter, B.T., Terrin, M.C., Dalman, R.L.: Medical management of small abdominal aortic aneurysms. Circulation 117, 1883 (2008)

    Article  Google Scholar 

  6. Davies, M.J.: Aortic aneurysm formation: lessons from human studies and experimental models. Circulation 98, 193–195 (1998)

    Article  Google Scholar 

  7. Wilmink, W.B.M., Quick, C.R.G., Hubbard, C.S., Day, N.E.: The influence of screening on the incidence of ruptured abdominal aortic aneurysms. J. Vasc. Surg. 30, 203–208 (1999)

    Article  Google Scholar 

  8. Carrell, T.W.G., Smith, A., Burnand, K.G.: Experimental techniques and models in the study of the development and treatment of abdominal aortic aneurysms. J. Surg. 86, 305–312 (1999)

    Google Scholar 

  9. Raghavan, M.L, Vorp, D.A.: Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. J. Biomech. 33, 475–482 (2000)

    Article  Google Scholar 

  10. Powell, J.T, Brady, A.R.: Detection, management and prospects for the medical treatment of small abdominal aortic aneurysms. Arteriosclerosis Thromb. Vasc. Biol. 24, 241–245 (2004)

    Article  Google Scholar 

  11. Powell, J.T., Gotensparre, S.M., Sweeting, M.J., Brown, L.C., Fowkes, F.G., Thompson, S.G.: Rupture rates of small abdominal aortic aneurysms: a systematic review of the literature. Eur. J. Vasc. Endovasc. Surg. 41, 2–10 (2011)

    Article  Google Scholar 

  12. Darling, R.C., Messina, C.R., Brewster, D.C., Ottinger, L.W.: Autopsy study of unoperated abdominal aortic aneurysms: the case for early resection. Circulation 56, 161–164 (1977)

    Google Scholar 

  13. Humphrey, J.D, Taylor, C.A.: Intracranial and abdominal aortic aneurysms: Similarities, differences, and need for a new class of computational models. Ann. Rev. Biomed. Eng. 10, 221–246 (2008)

    Article  Google Scholar 

  14. O’Connell, M.K., Murthy, S., Phan, S., Xu, C., Buchanan, J., Spilker, R., Dalman, R.L., Zarins, C.K., Denk, W., Taylor, C.A.: The three-dimensional micro- and nanostructure of the aortic medial lamellar unit measured using 3D confocal and electron microscopy imaging. Matrix Biology 27, 171–181 (2008)

    Article  Google Scholar 

  15. Watton, P.N., Hill, N.A., Heil, M.: A mathematical model for the growth of the abdominal aortic aneurysm. Biomech. Model. Mechanobiol. 3, 98–113 (2004)

    Article  Google Scholar 

  16. Watton, P.N., Hill, N.A.: Evolving mechanical properties of a model of abdominal aortic aneurysm. Biomech. Model. Mechanobiol. 8, 25–42 (2009)

    Article  Google Scholar 

  17. Zeinali-Davarani, S., Sheidaei, A., Baek, S.: A finite element model of stress-mediated vascular adaptation: application to abdominal aortic aneurysms. Comput. Methods Biomech. Biomed. Eng. 14, 803–817 (2011)

    Article  Google Scholar 

  18. Sheidaei, A., Hunley, S.C., Zeinali-Davarani, S., Raguin, L.G., Baek, S.: Simulation of abdominal aortic aneurysm growth with updating hemodynamic loads using a realistic geometry. Med. Eng. Phys. 33, 80–88 (2011)

    Article  Google Scholar 

  19. Chiquet, M.: Regulation of extracellular matrix gene expression by mechanical stress. Matrix Biology 18, 417–426 (1999)

    Article  Google Scholar 

  20. Armentano, R., Barra, J., Levenson, J., Simon, A., Pichel, R.: Arterial wall mechanics in conscious dogs: assessment of viscous, inertial and elastic moduli to characterize aortic wall behaviour. Circ. Res. 76, 468–478 (1995)

    Article  Google Scholar 

  21. Shadwick, R.: Mechanical design in arteries. J. Exp. Biology 202, 3305–3313 (1999)

    Google Scholar 

  22. Raghavan, M.L., Webster, M., Vorp, D.A.: Ex-vivo bio-mechanical behavior of AAA: assessment using a new mathematical model. Ann. Biomed. Eng. 24, 573–582 (1999)

    Article  Google Scholar 

  23. Kakisis, J.D., Liapis, C.D., Sumpio, B.E.: Effects of cyclic strain on vascular cells. Endothelium 11, 17–28 (2004)

    Article  Google Scholar 

  24. Gleason, R.L, Humphrey, J.D.: A 2d constrained mixture model for arterial adaptations to large changes in flow, pressure and axial stretch. Math. Med. Biology 22, 347–369 (2005)

    Article  MATH  Google Scholar 

  25. Gupta, V., Grande-Allen, K.J.: Effects of static and cyclic loading in regulating extracellular matrix synthesis by cardiovascular cells. Cardiovasc. Res. 72, 375–383 (2006)

    Article  Google Scholar 

  26. Alberts B., Bray D., Lewis J., Raff M., Roberts K., Watson J.D., (1994) Molecular biology of the cell, 4th edn. Garland Publishing, New York

    Google Scholar 

  27. McAnulty, R.J.: Fibroblasts and myofibroblasts: their source, function and role in disease. Int. J. Biochem. Cell Biology 39, 666–671 (2007)

    Article  Google Scholar 

  28. He, C.M, Roach, M.: The composition and mechanical properties of abdominal aortic aneurysms. J. Vasc. Surg. 20, 6–13 (1993)

    Article  Google Scholar 

  29. Shimizu, K., Mitchell, R.N., Libby, P.: Inflammation and cellular immune responses in abdominal aortic aneurysms. Arteriosclerosis Thromb. Vasc. Biology 26, 987–994 (2006)

    Article  Google Scholar 

  30. Nissen, R., Cardinale, G.J., Udenfriend, S.: Increased turnover of arterial collagen in hypertensive rats. Proc. Natl. Acad. Sci. U.S.A. Med. Sci. 75, 451–453 (1978)

    Article  Google Scholar 

  31. Arribas, S.M., Hinek, A., Gonzalez, M.C.: Elastic fibres and vascular structure in hypertension. Pharm. Ther. 111, 771–791 (2006)

    Article  Google Scholar 

  32. Holzapfel, G.A., Gasser, T.C., Ogden, R.W.: A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. 61, 1–48 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  33. Watton, P.N., Ventikos, Y., Holzapfel, G.A.: Modelling the growth and stabilisation of cerebral aneurysms. Math. Med. Biology 26, 133–164 (2009)

    Article  MATH  Google Scholar 

  34. Watton, P.N, Ventikos, Y.: Modelling evolution of saccular cerebral aneurysms. J. Strain Anal. 44, 375–389 (2009)

    Article  Google Scholar 

  35. Watton, P.N., Raberger, N.B., Holzapfel, G.A., Ventikos, Y.: Coupling the hemodynamic environment to the evolution of cerebral aneurysms: computational framework and numerical examples. ASME J. Biomech. Eng. 131, 101003 (2009)

    Article  Google Scholar 

  36. Watton, P.N., Selimovic, A., Raberger, N.B., Huang, P., Holzapfel, G.A., Ventikos, Y.: Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms. Biomech. Model. Mechanobiol. 11, 109–132 (2011)

    Article  Google Scholar 

  37. Watton, P.N., Ventikos, Y., Holzapfel, G.A.: Modelling cerebral aneurysm evolution, biomechanics and mechanobiology of aneurysms. Springer, Heidelberg (2011)

    Google Scholar 

  38. Dua, M.M, Dalman, R.L.: Hemodynamic influences on abdominal aortic aneurysm disease: application of biomechanics to aneurysm pathophysiology. Vasc. Pharm. 53, 11–21 (2010)

    Article  Google Scholar 

  39. Nakahashi, T.K., Tsao, K.H.P.S., Sho, E., Sho, M., Karwowski, J.K., Yeh, C., Yang, R.B., Topper, J.N., Dalman, R.L.: Flow loading inducesmacrophage antioxidative gene expression in experimental aneurysms. Arteriosclerosis Thromb. Vasc. Biology 22, 2017–2022 (2002)

    Article  Google Scholar 

  40. Hoshina, K., Sho, E., Sho, M., Nakahashi, T.K., Dalman, R.L.: Wall shear stress and strain modulate experimental aneurysm cellularity. J. Vasc. Surg. 37, 1067–1074 (2003)

    Google Scholar 

  41. Sho, E., Sho, M., Hoshina, K., et al.: Hemodynamic forces regulate mural macrophage infiltration in experimental aortic aneurysms. Exp. Mol. Pathol. 76, 108–116 (2004)

    Google Scholar 

  42. Heil, M.: The stability of cylindrical shells conveying viscous flow. J. Fluids Struct. 10, 173–196 (1996)

    Article  Google Scholar 

  43. Watton, P.N.: Mathematical modelling of the abdominal aortic aneurysm. Ph.D. Thesis, Department of Mathematics, University of Leeds, Leeds, UK (2002)

    Google Scholar 

  44. Watton, P.N., Ventikos, Y., Holzapfel, G.A.: Modelling the mechanical response of elastin for arterial tissue. J. Biomech. 42, 1320–1325 (2009)

    Article  Google Scholar 

  45. Humphrey, J.D.: Remodelling of a collagenous tissue at fixed lengths. J. Biomech. Eng. 121, 591–597 (1999)

    Article  Google Scholar 

  46. Gruttmann, F., Taylor, R.L.: Theory and finite element formulation of rubberlike membrane shells using principal stretches. Int. J. Numer. Methods Eng. 35, 1111–1126 (1992)

    Article  MATH  Google Scholar 

  47. Huang, H.: Haemodynamics in diseased arteries: effects on plaque and aneurysm progression by advanced imaging and modelling techniques. Ph.D. Thesis, Department of Engineering Science, University of Oxford, Oxford, UK (2010)

    Google Scholar 

  48. Patakar, S.V.: Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, Washington – New York – London. McGraw Hill Book Company, New York (1980)

    Google Scholar 

  49. Ferziger J.H, Peric M., (2002) Computational methods for fluid dynamics, 3rd edn. Springer, Heidelberg

    Google Scholar 

  50. Hutchinson, B.R, Raithby, G.D.: A multigrid method based on the additive correction strategy. Numer. Heat Transf. 9, 511–537 (1986)

    Google Scholar 

  51. Cebral, J.R., Castro, M.A., Appanaboyina, S., Putman, C.M., Millan, D., Frangi, A.F.: Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: technique and sensitivity. IEEE Trans. Med. Imaging 24, 457–467 (2005)

    Article  Google Scholar 

  52. Fisher, C., Rossmann, J.S.: Effect of non-newtonian behavior on hemodynamics of cerebral aneurysms. ASME J. Biomech. Eng. 131, 091004 (2009)

    Article  Google Scholar 

  53. Chatziprodromou, I., Tricoli, A., Poulikakos, D., Ventikos, Y.: Haemodynamics and wall remodelling of a growing cerebral aneurysm: a computational model. J. Biomech. 40, 412–426 (2007)

    Article  Google Scholar 

  54. Oshima, M., Torii, R., Kobayashia, T., Taniguchic, N., Takagid, K.: Finite element simulation of blood flow in the cerebral artery. Comput. Methods Appl. Mech. Eng. 191, 661–671 (2001)

    Article  MATH  Google Scholar 

  55. Reymond, P., Merenda, F., Perren, F., Rufenacht, D., Stergiopulos, N.: Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 297, H208–H222 (2009)

    Article  Google Scholar 

  56. Villa-Uriol M.C., Berti G., Hose D.R., Marzo A., Chiarini A., Penrose J., Pozo J., Schmidt J.G., Singh P., Lycett R., Larrabide I., Frangi A.F.: @neurist complex information processing toolchain for the integrated management of cerebral aneurysms. Interface Focus 1, 308–319 (2011)

    Google Scholar 

  57. Reymond P., Bohraus Y., Perren F., Lazeyras F., Stergiopulos N., (2011) Validation of a patient-specific one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 301, H1173–H1182

    Google Scholar 

  58. Wang, J.H.C, Thampaty, B.P.: An introductory review of cell mechanobiology. Biomech. Model. Mechanobiol. 5, 1–16 (2006)

    Article  Google Scholar 

  59. Chiquet, M., Renedo, A.S., Huber, F., Flück, M.: How do fibroblasts translate mechanical signals into changes in extracellular matrix production?. Matrix Biology 22, 73–80 (2003)

    Article  Google Scholar 

  60. Sotoudeh, M., Jalali, S., Usami, S., Shyy, J.Y., Chien, S.: A strain device imposing dynamic and uniform equi-biaxial strain to cultured cells. Ann. Biomed. Eng. 26, 181–189 (1998)

    Article  Google Scholar 

  61. Shin, H.Y., Gerritsen, M.E., Bizios, R.: Regulation of endothelial cell proliferation and apoptosis by cyclic pressure. Ann. Biomed. Eng. 30, 297–304 (2002)

    Article  Google Scholar 

  62. Länne, T., Sonesson, B., Bergqvist, D., Bengtsson, H., Gustafsson, D.: Diameter and compliance in the male human abdominal aorta: influence of age and aortic aneurysm. Eur. J. Vasc. Surg. 6, 178–184 (1992)

    Article  Google Scholar 

  63. Cummins, P.M., von Offenberg Sweeney, N., Killeen, M.T., Birney, Y.A., Redmond, E.M., Cahill, P.A.: Cyclic strain-mediated matrix metalloproteinase regulation within the vascular endothelium: a force to be reckoned with. Am. J. Physiol. Heart Circ. Physiol. 292, H28–H42 (2007)

    Google Scholar 

  64. Hsiai, T.K.: Mechanical transduction coupling between endothelial and smooth muscle cells: role of hemodynamic forces. Am. J. Physiol. Cell Physiol. 294, C695–C661 (2008)

    Article  Google Scholar 

  65. Zeinali-Davarani, S., Raguin, L.G., Baek, S.: An inverse optimization approach toward testing different hypotheses of vascular homeostasis using image-based models. Int. J. Struct. Changes Solids Mech. Appl. 3, 33–34 (2011)

    Google Scholar 

  66. Schmid, H., Watton, P.N., Maurer, M.M., Wimmer, J., Winkler, P., Wang, Y.K., Roehrle, O., Itskov, M.: Impact of transmural heterogeneities on arterial adaptation: application to aneurysm formation. Biomech. Model. Mechanobiol. 9, 295–315 (2010)

    Article  Google Scholar 

  67. Schmid, H., Grytsan, A., Postan, E., Watton, P.N., Itskov, M.: Influence of differing material properties in media and adventitia on arterial adaption: application to aneurysm formation and rupture. Comput. Methods Biomech. Biomed. Eng. (2011). DOI:10.1080/10255842.2011.603309

  68. Rodriguez, Z.M., Kenny, P., Gaynor, L.: Improved characterisation of aortic tortuosity. Med. Eng. Phys. 33, 1712–1719 (2011)

    Google Scholar 

  69. Pappu, S., Dardik, A., Tagare, H., Gusberg, R.J.: Beyond fusiform and saccular: a novel quantitative tortuosity index may help classify aneurysm shape and predict aneurysm rupture potential. Ann. Vasc. Surg. 22, 88–97 (2008)

    Article  Google Scholar 

  70. Georgakarakos E., Ioannou C.V., Kamarianakis Y., Papaharilaou Y., Kostas T., Manousaki E., Katsamouris A.N.: The role of geometric parameters in the prediction of abdominal aortic aneurysm wall stress. Eur. J. Vasc. Endovasc. Surg. 39, 42–48 (2010)

    Article  Google Scholar 

  71. Shum, J., Martufi, G., Di Martino, E., Washington, C.B., Grisafi, J., Muluk, S.C., Finol, E.A.: Quantitiatve assessment of abdominal aortic aneurysm geometry. Ann. Biomed. Eng. 39, 277–286 (2011)

    Article  Google Scholar 

  72. Dougherty, G., Johnson, M.J.: Clinical validation of three-dimensional tortuosity metrics based on the minimum curvature of approximating polynomial splines. Med. Eng. Phys. 30, 190–198 (2008)

    Article  Google Scholar 

  73. Dobrin, P.B., Schwarz, T.H., Baker, W.H.: Mechanisms of arterial and aneurysmal tortuosity. Surgery 104, 568–571 (1998)

    Google Scholar 

  74. Wang, J.H.C., Goldschmidt-Clermont, P., Yin, F.C.P.: Contractility affects stress fiber remodeling and reorientation of endothelial cells subjected to cyclic mechanical stretching. Ann. Biomed. Eng. 28, 1165–1171 (2000)

    Article  Google Scholar 

  75. Owatverot, T.B., Oswald, S.J., Chen, Y., WIllie, J.J.: Effect of combined cyclic stretch and fluid shear stress on endothelial cell morphological responses. ASME J. Biomech. Eng. 127, 374–382 (2005)

    Article  Google Scholar 

  76. Moore, J.E. Jr, Blirki, E., Sucui, A., Zhao, S., Burnier, M., Brunner, H.R., Meister, J.J.: A device for subjecting vascular endothelial cells to both fluid shear stress and circumferential cyclic stretch. Ann. Biomed. Eng. 22, 416–422 (1994)

    Article  Google Scholar 

  77. Lee, A.A., Graham, D.A., Dela Cruz, S., Ratcliffe, A., Karlon, W.J.: Fluid shear stress-induced alignment of cultured vascular smooth muscle cells. J. Biomech. Eng. 124, 37–43 (2002)

    Article  Google Scholar 

  78. Ng, C.P, Schwartz, M.A.: Mechanisms of interstitial flow-induced remodeling of fibroblast collagen cultures. Ann. Biomed. Eng. 34, 446–454 (2006)

    Article  Google Scholar 

  79. Wagenseil, J.E.: Cell orientation influences the biaxial mechanical properties of fibroblast populated collagen vessels. Ann. Biomed. Eng. 32, 720–731 (2004)

    Article  Google Scholar 

  80. Neidlinger-Wilke, C., Grood, E., Claes, L., Brand, R.: Fibroblast orientation to stretch begins within three hours. J. Orthop. Res. 20, 953–956 (2002)

    Article  Google Scholar 

  81. Dallon, J., Sherratt, J.A.: A mathematical model for fibroblast and collagen orientation. Bulletin Math. Biology 60, 101–130 (1998)

    Article  MATH  Google Scholar 

  82. Driessen, N.J.B., Wilson, W., Bouten, C.V.C., Baaijens, F.P.T.: A computational model for collagen fibre remodelling in the arterial wall. J. Theor. Biology 226, 53–64 (2004)

    Article  Google Scholar 

  83. Baaijens, F., Bouten, C., Driessen, N.: Modeling collagen remodeling. J. Biomech. 43, 166–175 (2010)

    Article  Google Scholar 

  84. Creane, A., Maher, E., Sultan, S., Hynes, N., Kelly, D.J., Lally, C.: A remodelling metric for angular fibre distributions and its application to diseased carotid bifurcations. Biomech. Model. Mechanobiol. 11(6), 869–882 (2012). doi:10.1007/s10237-011-0358-3

  85. Zulliger, M.A., Fridez, P., Hayashi, K., Stergiopulos, N.: A strain energy function for arteries accounting for wall composition and structure. J. Biomech. 37, 989–1000 (2004)

    Article  Google Scholar 

  86. Gasser, T.C., Ogden, R.W., Holzapfel, G.A.: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. Royal Soc. Interface 3, 15–35 (2006)

    Article  Google Scholar 

  87. Gasser, T.C.: An irreversible constitutive model for fibrous soft biological tissue: a 3-d microfiber approach with demonstrative application to abdominal aortic aneurysms. Acta Biomaterialia 7, 2457–2466 (2011)

    Article  Google Scholar 

  88. Asanuma, K., Magid, R., Johnson, C., Nerem, R.M., Galis, Z.S.: Uniaxial strain regulates matrix-degrading enzymes produced by human vascular smooth muscle cells. Am. J. Physiol. Heart Circ. Physiol. 284, H1778–H1784 (2003)

    Google Scholar 

  89. Zhang, J., Schmidt, J., Ryschich, E., Schumacher, H., Allenberg, J.R.: Increased apoptosis and decreased density of medial smooth muscle cells in human abdominal aortic aneurysms. Chin. Med. J. 116, 1549–1552 (2003)

    Google Scholar 

  90. Zulliger, M.A., Rachev, A., Stergiopulos, N.: A constitutive formulation of arterial mechanics including vascular smooth muscle tone. Am. J. Physiol. Heart Circ. Physiol. 287, H1335–1343 (2004)

    Article  Google Scholar 

  91. Baek, S., Valentín, A., Humphrey, J.D.: Biochemomechanics of cerebral vasospasm and its resolution: II constitutive relastions and model simulations. Ann. Biomed. Eng. 35, 1498–1509 (2007)

    Article  Google Scholar 

  92. Murtada, S., Kroon, M., Holzapfel, G.A.: A calcium-driven mechanochemical model for prediction of force generation in smooth muscle. Biomech. Model. Mechanobiol. 9, 749–762 (2010)

    Article  Google Scholar 

  93. Baek, S., Rajagopal, K.R., Humphrey, J.D.: A theoretical model of enlarging intracranial fusiform aneurysms. J. Biomech. Eng. 128, 142–149 (2006)

    Article  Google Scholar 

  94. Zeinali-Davarani, S., Raguin, L.G., Vorp, D.A., Baek, S.: Identification of in vivo material and geometric parameters of a human aorta: toward patient-specific modeling of abdominal aortic aneurysm. Biomech. Model. Mechanobiol. 10, 689–699 (2010)

    Article  Google Scholar 

  95. Myers, J.G., Moore, J.A., Ojha, M., Johnston, K.W., Ethier, C.R.: Factors influencing blood flow patterns in the human right coronary artery. Ann. Biomed. Eng. 29, 109–120 (2001)

    Article  Google Scholar 

  96. Mantha, A., Karmonik, C., Benndorf, G., Strother, C., Metcalfe, R.: Hemodynamics in a cerebral artery before and after the formation of an aneurysm. Am. J. Neuroradiol. 27, 1113–1118 (2006)

    Google Scholar 

  97. Doenitz, C.M.S.K., Zoephel, R., Brawanski, A.: A mechanism for rapid development of intracranial aneurysms: a case study. Neurosurgery 67, 1213–1221 (2010)

    Article  Google Scholar 

  98. Chien, S.: Mechanotransduction and endothelial cell homeostasis: the wisdom of the cell. Am. J. Physiol. Heart Circ. Physiol. 292, H1209–H1224 (2007)

    Article  Google Scholar 

  99. Chatzizisis, Y.S., Coskun, A.U., Jonas, M., Edelman, E.R., Feldman, C.L., Stone, P.H.: Role of endothelial shear stress in the natural history of coronary atherosclerosis and vascular remodeling: molecular, cellular, and vascular behavior. J. Am. Coll. Cardiol. 49, 2379–2393 (2007)

    Article  Google Scholar 

  100. Wang, D.H.J., Makaroun, M.S., Webster, M.W., Vorp, D.A.: Effect of intraluminal thrombus on wall stress in patient-specific models of abdominal aortic aneurysms. J. Vasc. Surg. 36, 598–604 (2002)

    Article  Google Scholar 

  101. Vorp, D.A., Lee, P.C., Wang, D.H., Makaroun, M.S., Nemoto, E.M., Ogawa, S., Webster, M.W.: Association of intraluminal thrombus in abdominal aortic aneurysm with local hypoxia and wall weakening. J. Vasc. Surg. 34, 291–299 (2001)

    Article  Google Scholar 

  102. Michel, J.B., Martin-Ventura, J.L., Egido, J., Sakalihasan, N., Treska, V., Lindholt, J., Allaire, E., Thorsteinsdottir, U., Cockerill, G., Swedenborg, J.: Novel aspects of the pathogenesis of aneurysms of the abdominal aorta in humans. Cardiovasc. Res. 90, 18–27 (2011)

    Article  Google Scholar 

  103. Humphrey, J.D., Holzapfel, G.A.: Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms. J. Biomech. 45(5), 805–814 http://dx.doi.org/10.1016/j.jbiomech.2011.11.021

  104. Xu, Z., Chen, N., Kamocka, M.M., Rosen, E.D., Alber, M.S.: Multiscale model of thrombus development. J. Royal Soc. Interface 5, 705–722 (2008)

    Article  Google Scholar 

  105. Xu, Z., Kamocka, M., Alber, M., Rosen, E.D.: Computational approaches to studying thrombus development. Arteriosclerosis Thromb. Vasc. Biology 31, 500–505 (2011)

    Article  Google Scholar 

  106. Biasetti, J., Hussain, F., Gasser, T.C.: Blood flow and coherent vortices in the normal and aneurysmatic aortas: a fluid dynamical approach to intra-luminal thrombus formation. J. Royal Soc. Interface 8, 1449–1461 (2011)

    Article  Google Scholar 

  107. Vande Geest, J.P., Sacks, M.S., Vorp, D.A.: A planar biaxial constitutive relation for the luminal layer of intra-luminal thrombus in abdominal aortic aneurysms. J. Biomech. 39, 2347–2354 (2006)

    Article  Google Scholar 

  108. van Dam, E.A., Dams, S.D., Peters, G.W.M., Rutten M., C.M., Schurink, G.W.H., Buth, J., van de Vosse, F.N.: Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus. Biomech. Model. Mechanobiol. 7, 127–137 (2008)

    Article  Google Scholar 

  109. Tong, J., Sommer, G., Regitnig, P., Holzapfel, G.A.: Dissection properties and mechanical strength of tissue components in human carotid bifurcations. Ann. Biomed. Eng. 39, 1703–1719 (2011)

    Article  Google Scholar 

  110. Sakalihasan, N., Michel, J.B.: Functional imaging of atherosclerosis to advance vascular biology. Eur. J. Vasc. Endovasc. Surg. 37, 728–734 (2009)

    Article  Google Scholar 

  111. Speelman, L., Bohra, A., Bosboom, E.M., Schurink, G.W., van de Vosse, F.N., Makaroun, M.S., Vorp, D.A.: Effects of wall calcifications in patient- specific wall stress analyses of abdominal aortic aneurysms. J. Biomech. Eng. 129, 105–109 (2007)

    Article  Google Scholar 

  112. Maier, A., Gee, M.W., Reeps, C., Eckstein, H.H., Wall, W.A.: Impact of calcifications on patient-specific wall stress analysis of abdominal aortic aneurysms. Biomech. Model. Mechanobiol. 9, 511–521 (2010)

    Article  Google Scholar 

Download references

Acknowledgments

Paul Watton is funded by The Centre of Excellence in Personalized Healthcare (funded by the Wellcome Trust and EPSRC, grant number WT 088877/Z/09/Z). This support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Engineering Science, Institute of Biomedical Engineering, University of Oxford, Oxford, UK

    Paul N. Watton & Yiannis Ventikos

  2. Department of Mathematics, Imperial College, London, UK

    Huifeng Huang

Authors
  1. Paul N. Watton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huifeng Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yiannis Ventikos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul N. Watton .

Editor information

Editors and Affiliations

  1. , Biomechanics Research Unit, University of Liège, Chemin des Chevreuils 1–BAT 52/3, Liège 1, 4000, Belgium

    Liesbet Geris

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Watton, P.N., Huang, H., Ventikos, Y. (2012). Multi-Scale Modelling of Vascular Disease: Abdominal Aortic Aneurysm Evolution. In: Geris, L. (eds) Computational Modeling in Tissue Engineering. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/8415_2012_143

Download citation

  • DOI: https://doi.org/10.1007/8415_2012_143

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32562-5

  • Online ISBN: 978-3-642-32563-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation