Skip to main content
SpringerLink
Log in

Damage and Failure of the Vascular Wall

  • Living reference work entry
  • First Online:
Encyclopedia of Continuum Mechanics

  • 122 Accesses

Synonyms

Decline and collapse of the vessel wall; Deterioration and breakdown of the vessel wall; Softening and fracture of the arterial wall

Definitions

Understanding the damage and failure of vascular tissue is critical to the sensitive and specific characterization of tissue injury tolerance. Such understanding would directly improve the design of cardiovascular medical devices and may also have many other implications on patient treatment. As with other biological tissues, the vessel wall is composed of cellular (endothelial cells, smooth muscle cells, fibroblasts, myofibroblasts, etc.) and extracellular matrix (ECM) (elastin, collagen, proteoglycans (PGs), fibronectin, fibrillin, etc.) constituents. Cells are primarily responsible for maintaining the arterial wall’s metabolism, while the ECM ensures its structural integrity. At high mechanical loads, collagen fibers and their interaction with the ECM dominate load carrying in the vascular wall. Specifically, the amount and...

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Armero F, Garikipati K (1996) An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. Int J Solids Struct 33:2863–2885

    Article  MathSciNet  Google Scholar 

  • Balzani D, Schröder J, Gross D (2006) Simulation of discontinuous damage incorporating residual stresses in circumferentially overstretched atherosclerotic arteries. Acta Biomater 2:609–618

    Article  Google Scholar 

  • Barenblatt GI (1962) The mathematical theory of equilibrium of cracks in brittle fracture. Adv Appl Mech 7:55–129

    Article  MathSciNet  Google Scholar 

  • Bažant ZP, Pijaudier-Cabot G (1988) Nonlocal continuum damage, localization instability and convergence. J Appl Mech 55:287–293

    Article  Google Scholar 

  • Bergel DH (1961) The static elastic properties of the arterial wall. J Physiol 156:445–457

    Article  Google Scholar 

  • Bingham C (1974) An antipodally symmetric distribution on the sphere. Ann Statist 2:1201–1225

    Article  MathSciNet  Google Scholar 

  • Calvo B, Peña E, Martínez MA, Doblaré M (2007) An uncoupled directional damage model for fibred biological soft tissues formulation and computational aspects. Int J Numer Methods Bioeng 69:2036–2057

    Article  MathSciNet  Google Scholar 

  • Calvo B, Peña E, Martins P, Mascarenhas T, Doblaré M, Natal Jorge RM, Ferreira A (2009) On modelling damage process in vaginal tissue. J Biomech 42:642–651

    Article  Google Scholar 

  • Carey D (1991) Control of growth and differentiation of vascular cells by extracellular matrix proteins. Ann Rev Physiol 53:161–177

    Article  Google Scholar 

  • Chuong CJ, Fung YC (1983) Three-dimensional stress distribution in arteries. J Biomech Eng 105:268–274

    Article  Google Scholar 

  • Clark JM, Glagov S (1985) Transmural organization of the arterial media: the lamellar unit revisited. Arteriosclerosis 5:19–34

    Article  Google Scholar 

  • Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch R Mech Anal 13:167–178

    Article  MathSciNet  Google Scholar 

  • Diamant J, Keller A, Baer E, Litt M, Arridge RGC (1972) Collagen: ultrastructure and its relation to mechanical properties as a function of ageing. Proc R Soc Lond B 180:293–315

    Article  Google Scholar 

  • Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104

    Article  Google Scholar 

  • Emery JL, Omens JH, McCulloch AD (1997a) Biaxial mechanics of the passively overstretched left ventricle. Am J Physiol 272:H2299–H2305

    Google Scholar 

  • Emery JL, Omens JH, McCulloch AD (1997b) Strain softening in rat left ventricular myocardium. J Biomech Eng 119:6–12

    Article  Google Scholar 

  • Federico S, Gasser TC (2010) Non-linear elasticity of biological tissues with statistical fibre orientation. J R Soc Interface 7:955–966

    Article  Google Scholar 

  • Ferrara A, Pandolfi A (2008) Numerical modeling of fracture in human arteries. Comput Methods Biomech Biomed Eng 11:553–567

    Article  Google Scholar 

  • Fessel G, Snedeker JG (2011) Equivalent stiffness after glycosaminoglycan depletion in tendon–an ultra-structural finite element model and corresponding experiments. J Theor Biol 268:77–83

    Article  Google Scholar 

  • Forsell C, Gasser TC (2011) Numerical simulation of the failure of ventricular tissue due to deep penetration: the impact of constitutive properties. J Biomech 44:45–51

    Article  Google Scholar 

  • Fratzl P (ed) (2008) Collagen – structure and mechanics. Springer, New York

    Google Scholar 

  • Fung YC, Fronek K, Patitucci P (1979) Pseudoelasticity of arteries and the choice of its mathematical expression. Am J Physiol 237:H620–H631

    Google Scholar 

  • Gasser TC (2011) An irreversible constitutive model for fibrous soft biological tissue: a 3D microfiber approach with demonstrative application to Abdominal Aortic Aneurysms. Acta Biomater 7:2457–2466

    Article  Google Scholar 

  • Gasser TC, Grytsan A (2017) Biomechanical modeling the adaptation of soft biological tissue. Cur Opinion Biomed Eng 1:71–77

    Article  Google Scholar 

  • Gasser TC, Holzapfel GA (2002) A rate-independent elastoplastic constitutive model for (biological) fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation. Comput Mech 29:340–360

    Article  Google Scholar 

  • Gasser TC, Holzapfel GA (2003a) Geometrically non-linear and consistently linearized embedded strong discontinuity models for 3D problems with an application to the dissection analysis of soft biological tissues. Comput Methods Appl Mech Eng 192:5059–5098

    Article  MathSciNet  Google Scholar 

  • Gasser TC, Holzapfel GA (2003b) Necking phenomena of a fiber-reinforced bar modeled by multisurface plasticity. In: Miehe C (ed) IUTAM symposium on computational mechanics of solid materials at large strains, proceedings of the IUTAM symposium held in Stuttgart, 20–24 Aug 2001, pp 211–220. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Gasser TC, Holzapfel GA (2005) Modeling 3D crack propagation in unreinfoced concrete using PUFEM. Comput Meth Appl Mech Eng 194:2859–2896

    Article  Google Scholar 

  • Gasser TC, Holzapfel GA (2006) Modeling dissection propagation in soft biological tissues. Eur J Mech A/Solids 25:617–633

    Article  MathSciNet  Google Scholar 

  • Gasser TC, Holzapfel GA (2007) Modeling dissection failure during balloon angioplasty. Ann Biomed Eng 35:711–723

    Article  Google Scholar 

  • Gasser TC, Holzapfel GA (2006) 3D crack propagation in unreinforced concrete. A new smoothing algorithm for tracking 3D crack surfaces. Comput Meth Appl Mech Eng 195:5198–5219

    Article  Google Scholar 

  • Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3:15–35

    Article  Google Scholar 

  • Gasser TC, Gudmundson P, Dohr G (2009) Failure mechanisms of ventricular tissue due to deep penetration. J Biomech 42:626–633

    Article  Google Scholar 

  • Gasser TC, Gallinetti S, Xing X, Forsell C, Swedenborg J, Roy J (2012) Spatial orientation of collagen fibers in the Abdominal Aortic Aneurysm wall and its relation to wall mechanics. Acta Biomater 8:3091–3103

    Article  Google Scholar 

  • Gathercole LGJ, Keller A, Shah JS (1974) Periodic wave pattern in native tendon collagen: correlation of polarising with scanning electron microscopy. J Microscopy 10:95–105

    Article  Google Scholar 

  • Hamedzadeh A, Gasser TC, Federico S (2018) On the constitutive modelling of recruitment and damage of collagen fibres in soft biological tissues. Eur J Mech Solids 72:483–496

    Article  MathSciNet  Google Scholar 

  • Hardin RH, Sloane NJA (1996) McLaren’s improved snub cube and other new spherical designs in three dimensions. Discret Comput Geom 15:429–441

    Article  MathSciNet  Google Scholar 

  • Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773–782

    Article  Google Scholar 

  • Hokanson J, Yazdani S (1997) A constitutive model of the artery with damage. Mech Res Commun 24:151–159

    Article  Google Scholar 

  • Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1–48

    Article  MathSciNet  Google Scholar 

  • Humphrey JD, Strumpf RK, Yin FCP (1990) Determination of constitutive relation for passive myocardium – part I and II. J Biomech Eng 112:333–346

    Article  Google Scholar 

  • Hurschler C, Loitz-Ramage B, Vanderby R Jr (1997) A structurally based stress-stretch relationship for tendon and ligament. J Biomech Eng 119:392–399

    Article  Google Scholar 

  • Ionescu I, Guilkey JE, Berzins M, Kirby RM, Weiss JA (2006) Simulation of soft tissue failure using the material point method. J Biomech Eng 128:917–94

    Article  Google Scholar 

  • Kachanov LM (1986) Introduction to continuum damage mechanics. Martinus Nijhoff Publishers, Dordrecht

    Book  Google Scholar 

  • Knörzer E, Folkhard W, Geercken W, Boschert C, Koch MH, Hilbert B, Krahl H, Mosler E, Nemetschek-Gansler H, Nemetschek T (1986) New aspects of the etiology of tendon rupture. An analysis of time-resolved dynamic-mechanical measurements using synchrotron radiation. Arch Orthop Trauma Surg 105:113–120

    Article  Google Scholar 

  • Langewouters GJ, Wesseling KH, Goedhard WJA (1984) The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J Biomech 17:425–435

    Article  Google Scholar 

  • Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16:1–12

    Article  Google Scholar 

  • Liao J, Vesely I (2007) Skewness angle of interfibrillar proteoglycans increases with applied load on mitral valve chordae tendineae. J Biomech 40:390–398

    Article  Google Scholar 

  • Marini G, Maier A, Reeps C, Eckstein H-H, Wall WA, Gee MW (2011) A continuum description of the damage process in the arterial wall of abdominal aortic aneurysms. Int J Numer Methods Bioeng 28:87–99

    Article  MathSciNet  Google Scholar 

  • Martufi G, Gasser TC (2011) A constitutive model for vascular tissue that integrates fibril, fiber and continuum levels. J Biomech 44:2544–2550

    Article  Google Scholar 

  • Ogden RW (1997) Non-linear elastic deformations. Dover, New York

    Google Scholar 

  • Ogden RW (2001) Elements of the theory of finite elasticity. In: Fu YB, Ogden RW (eds) Nonlinear elasticity theory and applications. Cambridge University Press, Cambridge, pp 1–57

    MATH  Google Scholar 

  • Oktay HS, Kang T, Humphrey JD, Bishop GG (1991) Changes in the mechanical behavior of arteries following balloon angioplasty. In: ASME 1991 biomechanics symposium, AMD-Vol 120. American Society of Mechanical Engineers

    Google Scholar 

  • Oliver J (1996) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: fundamentals. Int J Numer Methods Eng 39:3575–3600

    Article  Google Scholar 

  • Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44:1267–1282

    Article  Google Scholar 

  • Pena J, Martínez MA, Pena E (2011) A formulation to model the nonlinear viscoelastic properties of the vascular tissue. Acta Mech 217:63–74

    Article  Google Scholar 

  • Quinn KP, Winkelstein BA (2008) Altered collagen fiber kinematics define the onset of localized ligament damage during loading. J Appl Physiol 105:1881–1888

    Article  Google Scholar 

  • Redaelli A, Vesentini S, Soncini M, Vena P, Mantero S, Montevecchi FM (2003) Possible role of decorin glycosaminoglycans in fibril to fibril force transfer in relative mature tendons–a computational study from molecular to microstructural level. J Biomech 36:1555–1569

    Article  Google Scholar 

  • Rigozzi S, Mueller R, Snedeker JG (2009) Local strain measurement reveals a varied regional dependence of tensile tendon mechanics on glycosaminoglycan content. J Biomech 42:1547–1552

    Article  Google Scholar 

  • Rigozzi S, Mueller R, Snedeker JG (2010) Collagen fibril morphology and mechanical properties of the achilles tendon in two inbred mouse strains. J Anat 216:724–731

    Article  Google Scholar 

  • Roach MR, Burton AC (1957) The reason for the shape of the distensibility curve of arteries. Can J Biochem Physiol 35:681–690

    Article  Google Scholar 

  • Robinson PS, Huang TF, Kazam E, Iozzo RV, Birk DE, Soslowsky LJ (2005) Influence of decorin and biglycan on mechanical properties of multiple tendons in knockout mice. J Biomech Eng 127:181–185

    Article  Google Scholar 

  • Salunke NV, Topoleski LDT (1997) Biomechanics of atherosclerotic plaque. Crit Rev Biomed Eng 25:243–285

    Google Scholar 

  • Sasaki N, Odajima S (1996) Elongation mechanism of collagen fibrils and force-strain relations of tendon at each level of the structural hierarchy. J Biomech 29:1131–1136

    Article  Google Scholar 

  • Scott JE (2003) Elasticity in extracellular matrix ‘shape modules’ of tendon, cartilage, etc. A sliding proteoglycan-filament model. J Physiol 553(2):335–343

    Article  Google Scholar 

  • Scott JE (2008) Cartilage is held together by elastic glycan strings. Physiological and pathological implications. Biorheology 45:209–217

    Google Scholar 

  • Sokolis DP (2007) Passive mechanical properties and structure of the aorta: segmental analysis. Acta Physiol 190:277–289

    Article  Google Scholar 

  • Spencer AJM (1984) Constitutive theory for strongly anisotropic solids. In: Spencer AJM (ed) Continuum theory of the mechanics of fibre-reinforced composites. CISM Courses and Lectures. International Centre for Mechanical Sciences, vol 282. Springer, Wien, pp 1–32

    Chapter  Google Scholar 

  • Takamizawa K, Hayashi K (1987) Strain energy density function and uniform strain hypothesis for arterial mechanics. J Biomech 20:7–17

    Article  Google Scholar 

  • Tanaka E, Yamada H (1990) An inelastic constitutive model of blood vessels. Acta Mech 82:21–30

    Article  Google Scholar 

  • Vaishnav RN, Young JT, Janicki JS, Patel DJ (1972) Nonlinear anisotropic elastic properties of the canine aorta. Biophys J 12:1008–1027

    Article  Google Scholar 

  • Vesentini S, Redaelli A, Montevecchi FM (2005) Estimation of the binding force of the collagen molecule-decorin core protein complex in collagen fibril. J Biomech 38:433–443

    Article  Google Scholar 

  • Viano DC, King AI, Melvin JW, Weber K (1989) Injury biomechanics research: an essential element in the prevention of trauma. J Biomech 22:403–417

    Article  Google Scholar 

  • Volokh KY (2007) Prediction of arterial failure based on microstructural bi-layer fiber-matrix model with softening. J Biomech 41:447–453

    Article  Google Scholar 

  • Wells GN, Sluys LJ (2001) Three-dimensional embedded discontinuity model for brittle fracture. Int J Solids Struct 38:897–913

    Article  Google Scholar 

  • Wells GN, de Borst R, Sluys LJ (2002) A consistent geometrically non-linear approach for delamination. Int J Numer Methods Eng 54:1333–1355

    Article  MathSciNet  Google Scholar 

  • Wuyts FL, Vanhuyse VJ, Langewouters GJ, Decraemer WF, Raman ER, Buyle S (1995) Elastic properties of human aortas in relation to age and atherosclerosis: a structural model. Phys Med Biol 40:1577–1597

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. KTH Solid Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden

    T. Christian Gasser

  2. Faculty of Health Sciences, University of Southern Denmark, Odense, Denmark

    T. Christian Gasser

Authors
  1. T. Christian Gasser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Christian Gasser .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Andreas Öchsner

Section Editor information

  1. Faculty of Mechanical, Industrial and Maritime Engineering, "Ovidius" University of Constanta, Constanta, Romania

    Eduard-Marius Craciun

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Gasser, T.C. (2018). Damage and Failure of the Vascular Wall. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_243-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53605-6_243-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation