Structurally motivated damage models for arterial walls. Theory and application

Modeling, Simulation and Applications

Volumn 5, Issue , 2012, Pages 143-185

  Robertson, Anne M ^a   Hill, Michael R ^a   Li, Dalong ^b  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b ANSYS INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84874389120     PISSN: 20375255     EISSN: 20375263     Source Type: Book Series    
DOI: 10.1007/978-88-470-1935-5_6     Document Type: Article

References (125)

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.
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.
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.
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.
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.
6. Bergel D.H.: The static elastic properties of the arterial wall. The Journal of Physiology 156(3): 445-457, 1961.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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)
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.
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.
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.
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.
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.
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)
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.
26. Ericksen J.E., Rivlin R.S.: Large elastic deformations of homogeneous anisotropic materials. J. Rat. Mech. Anal. 3: 281-301, 1954.
27. Federico S., Herzog W.: Towards an analytical model of soft biological tissues. Journal of biomechanics 41(16): 3309-3313, 2008.
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.
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.
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.
31. Fonck E., Prod'hom 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.
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.
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.
34. Gasser C.T., Holzapfel G.: Modeling plaque fissuring and dissection during balloon angioplasty intervention. Annals of Biomedical Engineering 35(5): 711-723, 2007.
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.
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.
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.
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.
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.
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.
41. Greenwald S.E.: Ageing of the conduit arteries. The Journal of pathology 211(2): 157-172, 2007.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
53. Holzapfel G.A.: Nonlinear Solid Mechanics A Continuum Approach for Engineering. J. Wiley & Sons, 2000.
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.
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.
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.
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.
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.
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.
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.
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.
62. Kachanov L.: Time of rupture process under creep conditions. IVZ Akad. Nauk, S.S.R., Otd Tech Nauk 8: 26-31 (1958)
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)
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.
65. Krex D., Schackert H.K., Schackert G.: Genesis of cerebral aneurysms-an update. Acta Neurochirurgica 143(5): 429-448; discussion 448-429, 2001.
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.
67. Lanir Y.: Constitutive equations for fibrous connective tissues. Journal of biomechanics 16(1): 1-12, 1983.
68. Lee R.M.: Morphology of cerebral arteries. Pharmacology & therapeutics 66(1): 149-173, 1995.
69. Lematire J., Desmorat R.: Engineering damage mechanics: ductile, creep, fatigue and brittle failures. Springer, 2005.
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.
71. Li D., Robertson, A.: A structural multi-mechanism constitutive model for cerebral arterial tissue. Int. J. Solids Struct. 46: 2920-2928, 2009.
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.
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.
74. Li D., Robertson A.M.: A structural multi-mechanism damage model for cerebral arterial tissue. J. Biomech. Eng. 131: 8 pages, 2009. Doi: 10.1115/1.3202559
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.
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.
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.
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.
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)
80. Montes G.S.: Structural biology of the fibres of the collagenous and elastic systems. Cell Biol Int 20(1): 15-27, 1996.
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.
82. Mullins L.: Effect of stretching on the properties of rubber. Rubber Chem. Technol. 21: 281-300, 1948.
83. Mullins L.: Softening of rubber by deformation. Rubber Chemistry and Technology 42: 339-362, 1969.
84. Oktay H.: Continuum damage mechanics of balloon angioplasty. doctoral, University of Maryland, Baltimore County (1993)
85. O'Rourke M.: Mechanical principles in arterial disease. Hypertension 26: 2-9, 1995.
86. O'Rourke M.F.: Vascular mechanics in the clinic. Journal of biomechanics 36(5): 623-630, 2003.
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.
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.
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.
90. Reuterwall O.: Über die Elästizität der Gefäßwände und die Methoden ihrer näheren Prü-fung. Acta med. scand Suppl 2.: 1-175, 1921.
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.
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.
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.
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.
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.
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.
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.
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)
99. Sacks M.S., Sun W.: Multiaxial mechanical behavior of biological materials. Annual Review of Biomedical Engineering 5: 251-284, 2003.
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.
101. Schievink W.I., Roiter V.: Epidemiology of cervical artery dissection. Frontiers of neurology and neuroscience 20: 12-15, 2005.
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.
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.
104. Sherratt M.: Tissue elasticity and the ageing elastic fibre. AGE 31: 305-325, 2009.
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)
106. Sidorov S.: Finite element modeling of human artery tissue with a nonlinear multimechanism inelastic material. Ph.D. thesis, U. of Pittsburgh (2006)
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.
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)
109. Spencer A.J.M.: Theory of invariants. In: A.C. Eringen (ed.) Continuum Physics, vol. I, pp. 239-253. Academic Press, 1971.
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.
111. Wagenseil J., Mecham R.: Vascular extracellular matrix and arterial mechanics. Physiological Reviews 89(3): 957-989, 2009.
112. Watton P., Ventikos Y., Holzapfel G.: Modelling the mechanical response of elastin for arterial tissue. J. Biomech. 42: 1320-1325, 2009.
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.
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.
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).
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.
117. Wolinsky H., Glagov S.: Structural basis for the static mechanical properties of the aortic media. Circulation research 14: 400-413, 1964.
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.
119. Wulandana R., Robertson A.M.: An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech. Model. Mechanobiol. 4(4): 235-248, 2005.
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.
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.
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.
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)
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.
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.