Structurally motivated damage models for arterial walls. Theory and application

  • Anne M. Robertson
  • Michael R. Hill
  • Dalong Li
Part of the MS&A — Modeling, Simulation and Applications book series (MS&A, volume 5)


The mechanical integrity of the arterial wall is vital for the health of the individual. This integrity is in turn dependent on the state of the central load bearing components of the wall: collagen fibres, elastic fibres and smooth muscle. Of these, the elastic fibres, composed largely of the protein elastin, are viewed as responsible for the highly elastic behaviour of the wall at low loads [92]. The collagen fibres are recruited under increasing extension, leading to a highly nonlinear behaviour of the arterial wall [117]. They are responsible for the structural integrity of the wall at elevated physiological loads. Changes in the quantity, distribution, orientation and mechanical properties of these components (the microstructure) are known to occur as part of a healthy response to changing stimuli (e.g. growth and remodelling) as well as during pathological and damage processes in disease and aging. For example, degradation of the elastic fibres is linked to pathological conditions including cerebral aneurysms [12, 15, 20, 65], dissection aneurysms [101], arteriosclerosis [11, 44, 86, 113, 114], and complications from balloon angioplasty [84]. Age related arterial stiffening is attributed to degradation of the elastic fibres, possibly from fatigue failure [11, 30]. The subject of arterial damage is addressed in Sect. 6.4.


Wall Shear Stress Collagen Fibre Arterial Wall Second Harmonic Generation Elastic Fibre 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Alastrué V.,Martínez M.A., Doblaré M., Menzel A.: Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling. Journal of the Mechanics and Physics of Solids 57(1): 178–203, 2009.MATHCrossRefGoogle Scholar
  2. 2.
    Alastrué V., Sáez, P., Martínez, M.A., Doblaré, M.: On the use of the Bingham statistical distribution in microsphere-based constitutive models for arterial tissue. Mech Res Commun 37(8): 700–706, 2010.CrossRefGoogle Scholar
  3. 3.
    Avolio A., Jones D., Tafazzoli-Shadpour M.: Quantification of alterations in structure and function of elastin in the arterial media. Hypertension 32(1): 170–175, 1998.CrossRefGoogle Scholar
  4. 4.
    Baker C.J., Fiore A., Connolly E.S., Baker K.Z., Solomon R.A.: Serum elastase and alpha-1-antitrypsin levels in patients with ruptured and unruptured cerebral aneurysms. Neurosurgery 37(1): 56–61; discussion 61–52, 1995.CrossRefGoogle Scholar
  5. 5.
    Balzani D., Schröder J., Gross D.: Simulation of discontinuous damage incorporating residual stresses in circumferentially overstretched atherosclerotic arteries. Acta Biomater 2(6): 609–618, 2006.CrossRefGoogle Scholar
  6. 6.
    Bergel D.H.: The static elastic properties of the arterial wall. The Journal of Physiology 156(3): 445–457, 1961.Google Scholar
  7. 7.
    Betten J.: Formulation of anisotropic constitutive equations. In: J.P. Boehler (ed.) Applications of Tensor Functions in Solid Mechanics, CISM Courses and Lectures, 292, pp. 227–250. International Center for Mechanical Sciences, Springer-Verlag, 1984.Google Scholar
  8. 8.
    Brandt T., Morcher M., Hausser I.: Association of cervical artery dissection with connective tissue abnormalities in skin and arteries. Frontiers of neurology and neuroscience 20: 16–29, 2005.CrossRefGoogle Scholar
  9. 9.
    Broom N., Ramsey G., Mackie R., Martins B., Stehbens W.: A new biomechanical approach to assessing the fragility of the internal elastic lamina of the arterial wall. Connective Tissue Research 30(2): 143–155, 1993.CrossRefGoogle Scholar
  10. 10.
    Bullitt E., Lin N., Smith J., Zeng D., Winer E., Carey L., Lin W., Ewend M.: Blood vessel morphological changes depicted with mr angiography during treatment of brain metastases: a feasibility study. Radiology 40: 824–830, 2007.CrossRefGoogle Scholar
  11. 11.
    Busby D.E., Burton A.C.: The effect of age on the elasticity of the major brain arteries. Canadian journal of physiology and pharmacology 43: 185–202, 1965.CrossRefGoogle Scholar
  12. 12.
    Cajander S., Hassler O.: Enzymatic destruction of the elastic lamella at the mouth of the cerebral berry aneurysm? Acta Neruol Scand 53: 171–181, 1976.CrossRefGoogle Scholar
  13. 13.
    Campbell G., Roach M.: The use of ligament efficiency to model fenestrations in the internal elastic lamina of cerebral arteries. I–modelling scheme. J Biomech 16: 875–882, 1983.CrossRefGoogle Scholar
  14. 14.
    Campbell G., Roach M.: The use of ligament efficiency to model fenestrations in the internal elastic lamina of cerebral arteries. II–analysis of the spatial geometry. J Biomech 16: 883–91, 1983.CrossRefGoogle Scholar
  15. 15.
    Campbell G., Roach M.: A physical model for the formation of evaginations: a prospective precursor to the creation of saccular aneurysms. Stroke 15: 642–52, 1984.CrossRefGoogle Scholar
  16. 16.
    Castaneda-Zuniga W.R., Amplatz K., Laerum F., Formanek A., Sibley R., Edwards J., Vlodaver Z.: Mechanics of angioplasty: an experimental approach. RadioGraphics 1(3): 1–14 (1981)Google Scholar
  17. 17.
    Castaneda-Zuniga W.R., Formanek A., Tadavarthy M., Vlodaver Z., Edwards J.E., Zollikofer C., Amplatz K.: The mechanism of balloon angioplasty. Radiology 135(3): 565–571, 1980.Google Scholar
  18. 18.
    Chavez L., Takahashi A., Yoshimoto T., Su C.C., Sugawara T., Fujii Y.: Morphological changes in normal canine basilar arteries after transluminal angioplasty. Neurol Res 12(1): 12–16 (1990)Google Scholar
  19. 19.
    Chyatte D., Reilly J., Tilson M.D.: Morphometric analysis of reticular and elastin fibres in the cerebral arteries of patients with intracranial aneurysms. Neurosurgery 26(6): 939–943, 1990.CrossRefGoogle Scholar
  20. 20.
    Connolly E.S.J., Fiore A.J., Winfree C.J., Prestigiacoma C.J., Goldman J.E., Solomon R.A.: Elastin degradation in the superficial temporal arteries of patients with intracranial aneurysms reflects changes in plasma elastase. Neurosurgery 40(5): 903–908; discussion 908–909, 1997.CrossRefGoogle Scholar
  21. 21.
    Connors J.J., Wojak J.C.: Percutaneous transluminal angioplasty for intracranial atherosclerotic lesions: evolution of technique and short-term results. J Neurosurg 91(3): 415–423, 1999.CrossRefGoogle Scholar
  22. 22.
    Cortes D.H., Lake S.P., Kadlowec J.A., Soslowsky L.J., Elliott D.M.: Characterizing the mechanical contribution of fibre angular distribution in connective tissue: comparison of two modeling approaches. Biomech Model Mechanobiol 9: 651–658, 2010.CrossRefGoogle Scholar
  23. 23.
    Courtney T., Sacks M., Stankus J., Guan J., Wagner W.: Design and analysis of tissue engineering scaffolds that mimic soft tissue mechanical anisotropy. Biomaterials 27: 3631–3638, 2006.Google Scholar
  24. 24.
    Cox G., Kable E.: Second-harmonic imaging of collagen. In: D.J. Taatjes, B.T. Mossman (eds.) Cell Imaging Techniques: Methods and Protocols, Methods in Molecular Biology, vol. 319, pp. 15–35 (2006)CrossRefGoogle Scholar
  25. 25.
    Davis E.C.: Stability of elastin in the developing mouse aorta: a quantitative radioautographic study. Histochemistry and Cell Biology 100(1): 17–26, 1993.CrossRefGoogle Scholar
  26. 26.
    Ericksen J.E., Rivlin R.S.: Large elastic deformations of homogeneous anisotropic materials. J. Rat. Mech. Anal. 3: 281–301, 1954.MathSciNetMATHGoogle Scholar
  27. 27.
    Federico S., Herzog W.: Towards an analytical model of soft biological tissues. Journal of biomechanics 41(16): 3309–3313, 2008.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Finlay H., McCullough L., Canham P.: Three-dimensional collagen organization of human brain arteries at different transmural pressures. J. Vasc. Res. 32: 301–312, 1995.Google Scholar
  29. 29.
    Finlay H.M., McCullough L., Canham P.B.: Three-dimensional collagen organization of human brain arteries at different transmural pressures. J. Vasc. Res. 32: 301–312, 1995.Google Scholar
  30. 30.
    Fonck E., Feigl G.G., Fasel J., Sage D., Unser M., Rufenacht D.A., Stergiopulos N.: Effect of aging on elastin functionality in human cerebral arteries. Stroke 40(7): 2552–2556, 2009.CrossRefGoogle Scholar
  31. 31.
    [31] Fonck E., Prodhom G., Roy S., Augsburger L., Rufenacht D.A., Stergiopulos N.: Effect of elastin degradation on carotid wall mechanics as assessed by a constituent-based biomechanical model. American Journal Of Physiology. Heart And Circulatory Physiology 292(6): H2754–2763, 2007. CrossRefGoogle Scholar
  32. 32.
    Freed A., Einstein D., Vesely I.: Invariant formulation for dispersed transverse isotropy in aortic heart valves. Biomechanics and Modeling in Mechanobiology 4(2): 100–117, 2005.CrossRefGoogle Scholar
  33. 33.
    Gao L., Hoi Y., Swartz D.D., Kolega J., Siddiqui A., Meng H.: Nascent aneurysm formation at the basilar terminus induced by hemodynamics. Stroke; A Journal Of Cerebral Circulation 39(7): 2085–2090, 2008.CrossRefGoogle Scholar
  34. 34.
    Gasser C.T., Holzapfel G.: Modeling plaque fissuring and dissection during balloon angioplasty intervention. Annals of Biomedical Engineering 35(5): 711–723, 2007.CrossRefGoogle Scholar
  35. 35.
    Gasser C.T., Ogden R.W., Holzapfel G.A.: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal Of The Royal Society, Interface / The Royal Society 3(6): 15–35, 2006.CrossRefGoogle Scholar
  36. 36.
    Gasser T.C., Holzapfel G.: Arate-independent elastoplastic constitutive model for biological fibre-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation. Computational Mechanics 29(4-5): 340–360, 2002.MATHCrossRefGoogle Scholar
  37. 37.
    Gleason R.L., Humphrey J.: A 2D constrained mixture model for arterial adaptations to large changes in flow, pressure and axial stretch. Mathematical Medicine And Biology: A Journal Of The IMA 22(4): 347–369, 2005.MATHCrossRefGoogle Scholar
  38. 38.
    Gleason R.L., Taber L.A., Humphrey J.D.: A 2-d model of flow-induced alterations in the geometry, structure, and properties of carotid arteries. Journal of Biomechanical Engineering 126(3): 371–381, 2004.CrossRefGoogle Scholar
  39. 39.
    Goktepe S., Miehe C.: A micro-macro approach to rubber-like materials. part iii: The microsphere model of anisotropic mullins-type damage. Journal of the Mechanics and Physics of Solids 53(10): 2259–2283, 2005.MathSciNetCrossRefGoogle Scholar
  40. 40.
    Gonzalez J., Briones A., Starcher B., Conde M., Somoza B., Daly C., Vila E., McGrath I., Arribas S.: Influence of elastin on rat small artery mechanical properties. Exp Physiol 90: 463–8, 2005.CrossRefGoogle Scholar
  41. 41.
    Greenwald S.E.: Ageing of the conduit arteries. The Journal of pathology 211(2): 157–172, 2007.CrossRefGoogle Scholar
  42. 42.
    Gundiah N., Ratcliffe M.B., Pruitt L.: Determination of strain energy function for arterial elastin: Experiments using histology and mechanical tests. Journal of Biomechanics 40(3): 586–594, 2007.CrossRefGoogle Scholar
  43. 43.
    Gundiah N., Ratcliffe M.B., Pruitt L.A.: The biomechanics of arterial elastin. Journal of the Mechanical Behavior of Biomedical Materials 2(3): 288–296, 2009.CrossRefGoogle Scholar
  44. 44.
    Hadjinikolaou L., Kotidis K., Galinanes M.: Relationship between reduced elasticity of extracardiac vessels and left main stem coronary artery disease. European heart journal 25(6): 508–513, 2004.CrossRefGoogle Scholar
  45. 45.
    Hart W., Goldbaum M., Cote B., Kube P., Nelson M.: Measurement and classification of retinal vascular tortuosity. International Journal of Medical Informatics 53: 239–252, 1999.CrossRefGoogle Scholar
  46. 46.
    Hashimoto N., Kim C., Kikuchi H., Kojima M., Kang Y., Hazama F.: Experimental induction of cerebral aneurysms in monkeys. Journal of Neurosurgery 67(6): 903–905, 1987.CrossRefGoogle Scholar
  47. 47.
    Hassler O.: Morphological studies on the large cerebral arteries, with reference to the aetiology of subarachnoid haemorrhage. Acta psychiatrica Scandinavica 154: 1–145, 1961.Google Scholar
  48. 48.
    Higashida R.T., Halbach V.V., Dowd C.F., Dormandy B., Bell J., Hieshima G.B.: Intravascular balloon dilatation therapy for intracranial arterial vasospasm: patient selection, technique, and clinical results. Neurosurg Rev 15(2): 89–95, 1992.CrossRefGoogle Scholar
  49. 49.
    Hill M., Robertson A.M.: Combined histological and mechanical evaluation of isotropic damage to elastin in cerebral arteries. In: 6th World Congress on Biomechanics. Singapore, 2010.Google Scholar
  50. 50.
    Hill M., Robertson A.: Abrupt recruitment of medial collagen fibres in the rabbit carotid artery – SBC2011-5341. Proceedings of the ASME 2011 Summer Bioengineering Conference (SBC2011), June 22–25, Nemacolin Woodlands Resort. Farmington, PA, USA, 2 pages, 2011. Google Scholar
  51. 51.
    Holzapfel A.P.G.A.: Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. Journal of Biomechanical Engineering 130(6): 061,006–061,012, 2008.Google Scholar
  52. 52.
    Holzapfel G., Gasser T., Ogden R.: Anew constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity 61(1–3): 1–48, 2000.MathSciNetMATHCrossRefGoogle Scholar
  53. 53.
    Holzapfel G.A.: Nonlinear Solid Mechanics A Continuum Approach for Engineering. J. Wiley & Sons, 2000.MATHGoogle Scholar
  54. 54.
    Holzapfel G.A., Ogden R.W.: Constitutive modelling of arteries. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466(2118): 1551–1597, 2010.MathSciNetMATHCrossRefGoogle Scholar
  55. 55.
    Holzapfel G.A., Ogden R.W.: Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta. Journal of The Royal Society Interface 7(46): 787–799, 2010.CrossRefGoogle Scholar
  56. 56.
    Holzapfel G.A., Sommer G., Gasser C.T., Regitnig P.: Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling. Am. J. Physiol. Heart Circ. Physiol. 289: H2048–H2058, 2005.CrossRefGoogle Scholar
  57. 57.
    Honma Y., Fujiwara T., Irie K., Ohkawa M., Nagao S.: Morphological changes in human cerebral arteries after pta for vasospasm caused by subarachnoid hemorrhage. Neurosurgery 36(6): 1073–1081, 1995.CrossRefGoogle Scholar
  58. 58.
    Humphrey J.D., Baek S., Niklason L.E.: Biochemomechanics of cerebral vasospasm and its resolution: I. a new hypothesis and theoretical framework. Annals of Biomedical Engineering 35(9): 1485–1497, 2007.CrossRefGoogle Scholar
  59. 59.
    Humphrey J.D., Rajagopal K.R.: A constrained mixture model for growth and remodeling of soft tissues. Mathematical Models and Methods in Applied Sciences 12(3): 407–430, 2002.MathSciNetMATHCrossRefGoogle Scholar
  60. 60.
    Humphrey J.D., Rajagopal K.R.: A constrained mixture model for arterial adaptations to a sustained step change in blood flow. Biomechanics And Modeling In Mechanobiology 2(2): 109–126, 2003.CrossRefGoogle Scholar
  61. 61.
    Jiang C.F., Avolio A.P.: Characterisation of structural changes in the arterial elastic matrix by a new fractal feature: directional fractal curve. Medical & biological engineering & computing 35(3): 246–252, 1997.CrossRefGoogle Scholar
  62. 62.
    Kachanov L.: Time of rupture process under creep conditions. IVZ Akad. Nauk, S.S.R., Otd Tech Nauk 8: 26–31 (1958)Google Scholar
  63. 63.
    Keeley F.W.: The synthesis of soluble and insoluble elastin in chicken aorta as a function of development and age effect of a high cholesterol diet. Canadian journal of biochemistry 57(11): 1273–1280 (1979)CrossRefGoogle Scholar
  64. 64.
    Kondo S., Hashimoto N., Kikuchi H., Hazama F., Nagata I., Kataoka H.: Cerebral aneurysms arising at nonbranching sites an experimental study. Stroke 28(2): 398–403; discussion 403–394, 1997.CrossRefGoogle Scholar
  65. 65.
    Krex D., Schackert H.K., Schackert G.: Genesis of cerebral aneurysms–an update. Acta Neurochirurgica 143(5): 429–448; discussion 448–429, 2001.CrossRefGoogle Scholar
  66. 66.
    Lanir Y.: A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues. Journal of biomechanics 12(6): 423–436, 1979.CrossRefGoogle Scholar
  67. 67.
    Lanir Y.: Constitutive equations for fibrous connective tissues. Journal of biomechanics 16(1): 1–12, 1983.CrossRefGoogle Scholar
  68. 68.
    Lee R.M.: Morphology of cerebral arteries. Pharmacology & therapeutics 66(1): 149–173, 1995.CrossRefGoogle Scholar
  69. 69.
    Lematire J., Desmorat R.: Engineering damage mechanics: ductile, creep, fatigue and brittle failures. Springer, 2005.Google Scholar
  70. 70.
    Li D.: Structural multi-mechanism model with anisotropic damage for cerebral arterial tissues and its finite element modeling. Ph.D. thesis, University of Pittsburgh, 2009.Google Scholar
  71. 71.
    Li D., Robertson, A.: A structural multi-mechanism constitutive model for cerebral arterial tissue. Int. J. Solids Struct. 46: 2920–2928, 2009.MATHCrossRefGoogle Scholar
  72. 72.
    Li D., Robertson, A.M.: Finite element modeling of cerebral angioplasty using a multimechanism structural damage model. In: Proceedings of the ASME 2009 Summer Bioengineering Conference (SBC-2009), 2009.Google Scholar
  73. 73.
    Li D., Robertson A.M.: A structural damage model for cerebral arterial tissue and angioplasty simulation. In: 10th US National Congress on Computational Mechanics (USNCCM X), 2009.Google Scholar
  74. 74.
    Li D., Robertson A.M.: A structural multi-mechanism damage model for cerebral arterial tissue. J. Biomech. Eng. 131: 8 pages, 2009. Doi: 10.1115/1.3202559Google Scholar
  75. 75.
    Li D., Robertson A.M., Guoyu L.: Finite element modeling of cerebral angioplasty using a structural multi-mechanism anisotropic damage model. submitted for publication, 2011.Google Scholar
  76. 76.
    Meng H., Swartz D.D., Wang Z., Hoi Y., Kolega J., Metaxa E.M., Szymanski M.P., Yamamoto J., Sauvageau E., Levy E.I.: A model system for mapping vascular responses to complex hemodynamics at arterial bifurcations in vivo. Neurosurgery 59(5): 1094–100; discussion 1100–1, 2006.Google Scholar
  77. 77.
    Meng H., Wang Z., Hoi Y., Gao L., Metaxa E., Swartz D.D., Kolega J.: Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation. Stroke 38(6): 1924–1931, 2007.CrossRefGoogle Scholar
  78. 78.
    Miehe C.: Discontinuous and continuous damage evolution in ogden-type large-strain elastic materials. Eur. J. Mech. A/Solids 14(5): 697–720, 1995.MATHGoogle Scholar
  79. 79.
    Mohan D., Melvin J.W.: Failure properties of passive human aortic tissue. i–uniaxial tension tests. Journal of biomechanics 15(11): 887–902 (1982)CrossRefGoogle Scholar
  80. 80.
    Montes G.S.: Structural biology of the fibres of the collagenous and elastic systems. Cell Biol Int 20(1): 15–27, 1996.CrossRefGoogle Scholar
  81. 81.
    Morimoto M., Miyamoto S., Mizoguchi A., Kume N., Kita T., Hashimoto N.: Mouse model of cerebral aneurysm: experimental induction by renal hypertension and local hemodynamic changes. Stroke; A Journal Of Cerebral Circulation 33(7): 1911–1915, 2002.CrossRefGoogle Scholar
  82. 82.
    Mullins L.: Effect of stretching on the properties of rubber. Rubber Chem. Technol. 21: 281–300, 1948.CrossRefGoogle Scholar
  83. 83.
    Mullins L.: Softening of rubber by deformation. Rubber Chemistry and Technology 42: 339–362, 1969.CrossRefGoogle Scholar
  84. 84.
    Oktay H.: Continuum damage mechanics of balloon angioplasty doctoral, University of Maryland, Baltimore County (1993)Google Scholar
  85. 85.
    O’Rourke M.: Mechanical principles in arterial disease. Hypertension 26: 2–9, 1995.CrossRefGoogle Scholar
  86. 86.
    O’Rourke M.F.: Vascular mechanics in the clinic. Journal of biomechanics 36(5): 623–630, 2003.CrossRefGoogle Scholar
  87. 87.
    Peña E., Alastrué V., Laborda A., Martínez M.A., Doblaré M.: A constitutive formulation of vascular tissue mechanics including viscoelasticity and softening behaviour. Journal of biomechanics 43(5): 984–989, 2010.CrossRefGoogle Scholar
  88. 88.
    Peña E., Peña J.A., Doblaré M.: On the mullins effect and hysteresis of fibreed biological materials: A comparison between continuous and discontinuous damage models. International Journal of Solids and Structures 46(7–8): 1727–1735, 2009.MATHCrossRefGoogle Scholar
  89. 89.
    Rachev A., Hayashi K.: Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Annals of Biomedical Engineering 27(4): 459–468, 1999.CrossRefGoogle Scholar
  90. 90.
    Reuterwall O.: Über die Elästizität der Gefäßwände und die Methoden ihrer näheren Prü-fung. Acta med. scand Suppl 2.: 1–175, 1921.Google Scholar
  91. 91.
    Rhodin J.A.G.: Architecture of the vessel wall. In: R.M. Berne, N. Sperelakis (eds.) Vascular Smooth Muscle, The Cardiovascular System, vol. Vol 2 of Handbook of Physiology, Sect. 2: The Cardiovascular System., pp. 1–31. APS, Baltimore, 1979.Google Scholar
  92. 92.
    Roach M.R., Burton A.C.: The reason for the shape of the distensibility curves of arteries. Canadian journal of biochemistry and physiology 35(8): 681–690, 1957.CrossRefGoogle Scholar
  93. 93.
    Roach M.R., Burton A.C.: The reason for the shape of the distensibility curves of arteries. Can. J. Biochem. Physiol. 35: 681–690, 1957.CrossRefGoogle Scholar
  94. 94.
    Rodriguez J., Goicolea J.M., Gabaldon F.: A volumetric model for growth of arterial walls with arbitrary geometry and loads. Journal of biomechanics 40(5): 961–971, 2007.CrossRefGoogle Scholar
  95. 95.
    Rodríguez J., Martufi G., Doblaré M., Finol E.: The effect of material model formulation in the stress analysis of abdominal aortic aneurysms. Annals of Biomedical Engineering 37(11): 2218–2221, 2009.CrossRefGoogle Scholar
  96. 96.
    Ronchetti I., Alessandrini A., Contri M., Fornieri C., Mori G., Quaglino D., Valdre U.: Study of elastic fibre organization by scanning force microscopy. Matrix Biol 17: 75–83, 1988.CrossRefGoogle Scholar
  97. 97.
    Sacks M.S.: Incorporation of experimentally-derived fibre orientation into a structural constitutive model for planar-collagenous tissues. Journal of Biomechanical Engineering-Transactions of the Asme 125(2): 280–287, 2003.CrossRefGoogle Scholar
  98. 98.
    Sacks M.S., Smith D.B., Hiester E.D.: A SALS device for planar connective tissue microstructural analysis. Ann. Biomed. Eng. 25: 678–689 (1997)CrossRefGoogle Scholar
  99. 99.
    Sacks M.S., Sun W.: Multiaxial mechanical behavior of biological materials. Annual Review of Biomedical Engineering 5: 251–284, 2003.CrossRefGoogle Scholar
  100. 100.
    Samila Z., Carter S.: The effect of age on the unfolding of elastin lamellae and collagen fibres with stretch in human carotid arteries. Can. J. Physiol. Pharmacol. 59: 1050–1057, 1981.CrossRefGoogle Scholar
  101. 101.
    Schievink W.I., Roiter V.: Epidemiology of cervical artery dissection. Frontiers of neurology and neuroscience 20: 12–15, 2005.CrossRefGoogle Scholar
  102. 102.
    Scott S., Ferguson G.G., Roach M.R.: Comparison of the elastic properties of human intracranial arteries and aneurysms. Canadian journal of physiology and pharmacology 50(4): 328–332, 1972.CrossRefGoogle Scholar
  103. 103.
    Shapiro S., Endicott S., Province M., Pierce J., Campbell E.: Marked longevity of human lung parenchymal elastic fibres deduced from prevalence of d-aspartate and nuclear weaponsrelated radiocarbon. J Clin Invest 87: 1828–1834, 1991.CrossRefGoogle Scholar
  104. 104.
    Sherratt M.: Tissue elasticity and the ageing elastic fibre. AGE 31: 305–325, 2009.CrossRefGoogle Scholar
  105. 105.
    Shifren A., Mecham R.P.: The stumbling block in lung repair of emphysema: elastic fibre assembly. Proceedings of the American Thoracic Society 3(5): 428–433 (2006)CrossRefGoogle Scholar
  106. 106.
    Sidorov S.: Finite element modeling of human artery tissue with a nonlinear multimechanism inelastic material. Ph.D. thesis, U. of Pittsburgh (2006)Google Scholar
  107. 107.
    Simo J.C., Ju J.W.: Strain and stress-based continuum damage models- i. formulation. International Journal of Solids and Structures 23: 821–840, 1987.MATHCrossRefGoogle Scholar
  108. 108.
    Spencer A.: Constitutive theory for strongly anisotropic solids. In: A. Spencer (ed.) Continuum Theory of the Mechanics of Fibre-Reinforced Composites, CISM Courses and Lectures, vol. 282. Springer (1984)Google Scholar
  109. 109.
    [109] Spencer A.J.M.: Theory of invariants. In: A.C. Eringen (ed.) Continuum Physics, vol. I, pp. 239–253. Academic Press, 1971.Google Scholar
  110. 110.
    Valentin A., Cardamone L., Baek S., Humphrey J.: Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure. J. R. Soc. Interface 6: 293–306, 2009.CrossRefGoogle Scholar
  111. 111.
    Wagenseil J., Mecham R.: Vascular extracellular matrix and arterial mechanics. Physiological Reviews 89(3): 957–989, 2009.CrossRefGoogle Scholar
  112. 112.
    Watton P., Ventikos Y., Holzapfel G.: Modelling the mechanical response of elastin for arterial tissue. J. Biomech. 42: 1320–1325, 2009.CrossRefGoogle Scholar
  113. 113.
    Weber T., Auer J., Eber B., O’Rourke M.F.: Relationship between reduced elasticity of extracardiac vessels and left main stem coronary artery disease. European heart journal 25(21): 1966–1967, 2004.CrossRefGoogle Scholar
  114. 114.
    Weber T., Auer J., O’Rourke M.F. Kvas E., Lassnig E., Lamm G., Stark N., Rammer M., Eber B.: Increased arterial wave reflections predict severe cardiovascular events in patients undergoing percutaneous coronary interventions. European heart journal 26(24): 2657–2663, 2005.CrossRefGoogle Scholar
  115. 115.
    Wiechert L., Metzke R., Wall W.A.: Modeling the mechanical behaviour of lung tissue at the micro-level. Mechanics of Biological and bioinspired materials in Journal of Engineering Mechanics 135(5): 434–438, 2009. DOI  10.1061/(ASCE)0733-9399(2009)135:5(434).Google Scholar
  116. 116.
    Wojak J.C., Dunlap D.C., Hargrave K.R., DeAlvare L.A., Culbertson H.S., Connors J. Jr.: Intracranial angioplasty and stenting: long-term results from a single center. AJNR Am. J. Neuroradiol. 27(9): 1882–1892, 2006.Google Scholar
  117. 117.
    Wolinsky H., Glagov S.: Structural basis for the static mechanical properties of the aortic media. Circulation research 14: 400–413, 1964.CrossRefGoogle Scholar
  118. 118.
    Wulandana R., Robertson A.: Use of a multi-mechanism constitutive model for inflation of cerebral arteries. In: First Joint BMES/EMBS Conference, vol. 1, p. 235. Atlanta, GA, 1999.Google Scholar
  119. 119.
    Wulandana R., Robertson A.M.: An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech. Model. Mechanobiol. 4(4): 235–248, 2005.CrossRefGoogle Scholar
  120. 120.
    Zeng Z., Chung B.J., Durka M., Robertson A.M.: An in vitro device for evaluation of cellular response to flows found at the apex of arterial bifurcations. In: R. Rannacher, A. Sequeira (eds.) Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday. Springer-Verlag, New York, 2010.Google Scholar
  121. 121.
    Zipfel W.R., Williams R.M., Christie R., Nikitin A.Y., Hyman B.T., Webb W.W.: Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation. Proceedings of the National Academy of Sciences of the United States of America 100(12): 7075–7080, 2003.CrossRefGoogle Scholar
  122. 122.
    Zollikofer C.L., Chain J., Salomonowitz E., Runge W., Bruehlmann W.F., Castaneda-Zuniga W.R., Amplatz K.: Percutaneous transluminal angioplasty of the aorta. light and electron microscopic observations in normal and atherosclerotic rabbits. Radiology 151(2): 355–363, 1984.Google Scholar
  123. 123.
    Zoumi A., Lu X., Kassab G., Tromberg B.: Imaging coronary artery microstructure using second harmonic and two-photon fluorescence microscopy. Biophys J 87: 2778–2786 (2004)CrossRefGoogle Scholar
  124. 124.
    Zulliger M., Stergiopulos N.: Structural strain energy function applied to the ageing of the human aorta. Journal of biomechanics 40(14): 3061–3069, 2007.CrossRefGoogle Scholar
  125. 125.
    Zulliger M.A., Rachev A., Stergiopulos N.: A constitutive formulation of arterial mechanics including vascular smooth muscle tone. AmJ Physiol-Heart C 287(3): H1335–H1343, 2004.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Anne M. Robertson
    • 1
  • Michael R. Hill
    • 1
  • Dalong Li
    • 2
  1. 1.University of PittsburghPittsburghUSA
  2. 2.Ansys Inc.CanonsburgUSA

Personalised recommendations