Skip to main content

Structure-Based Constitutive Model of Coronary Media

  • Chapter
Book cover Structure-Based Mechanics of Tissues and Organs

Abstract

Blood vessel biomechanics is an essential and interdisciplinary research topic, incorporating disciplines ranging from nonlinear solid mechanics to anatomy, physiology, and pathology. Vascular mechanics is imperative for predicting vascular physiology and the way blood vessels interact mechanically with other organs. In addition, a number of vascular pathologies (e.g., atherosclerosis, hypertension, arterial aneurysms) have a pivotal biomechanical basis since they are initiated and propagated as a result of non-homeostatic mechanical loadings. Knowledge of the stress field in the blood vessel wall and its relation to strains and to loading imposed on the vessel cells will aid in understanding these diseases.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

  • Adcock S. Gaul, the genetic algorithm utility library. http://gaul.sourceforge.net (2004).

  • Azeloglu EU, Albro MB, Thimmappa VA, Ateshian GA, Costa KD. Heterogeneous transmural proteoglycan distribution provides a mechanism for regulating residual stresses in the aorta. Am J Physiol Heart Circ Physiol. 2008;294(3):H1197–205.

    Article  PubMed  CAS  Google Scholar 

  • Billiar KL, Sacks MS. Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II-a structural constitutive model. J Biomech Eng. 2000;122:327–35.

    Article  PubMed  CAS  Google Scholar 

  • Canham PB, Finlay HM, Dixon JG, Boughner DR, Chen A. Measurements from light and polarized light microscopy of human coronary arteries fixed at distending pressure. Cardiovasc Res. 1989;23(11):973–82.

    Article  PubMed  CAS  Google Scholar 

  • Canham PB, Finlay HM, Boughner DR. Contrasting structure of the saphenous vein and internal mammary artery used as coronary bypass vessels. Cardiovasc Res. 1997;34(3):557–67.

    Article  PubMed  CAS  Google Scholar 

  • Chen H, Lin Y, Zhao X, Lanir Y, Kassab GS. A micromechanics finite-strain constitutive model of fibrous tissue. J Mech Phys Solids. 2011a;59:1823–37.

    Article  PubMed  PubMed Central  Google Scholar 

  • Chen H, Liu Y, Slipchenko MN, Zhao X, Cheng J-X, Kassab GS. The layered structure of coronary adventitia under mechanical load. Biophys J. 2011b;101(11):2555–62.

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Chuong CJ, Fung YC. Three dimensional stress distribution in arteries. J Biomech Eng. 1983;105(3):268–74.

    Article  PubMed  CAS  Google Scholar 

  • Chuong CJ, Fung YC. On residual stresses in arteries. J Biomech Eng. 1986;108(2):189–92.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Dahl SLM, Vaughn ME, Niklason LE. An ultrastructural analysis of collagen in tissue engineered arteries. Ann Biomed Eng. 2007;35(10):1749–55.

    Article  PubMed  PubMed Central  Google Scholar 

  • Deng SX, Tomioka J, Debes JC, Fung YC. New experiments on shear modulus of elasticity of arteries. Am J Physiol. 1994;266(1 Pt 2):H1–10.

    PubMed  CAS  Google Scholar 

  • Fung YC. Stress-strain history relations of soft tissues in simple elongation. In: Fung YC, Perrone N, Anliker M, editors. Biomechanics—its foundations and objectives. Englewood Cliff: Prentice-Hall; 1972. p. 181–208.

    Google Scholar 

  • Fung YC. What are the residual stresses doing in our blood vessels? Ann Biomed Eng. 1991;19(3):237–49.

    Article  PubMed  CAS  Google Scholar 

  • Fung YC, Liu SQ. Strain distribution in small blood vessels with zero-stress state taken into consideration. Am J Physiol. 1992;262(2 Pt 2):H544–52.

    PubMed  CAS  Google Scholar 

  • Fung YC, Fronek K, Patitucci P. Pseudoelasticity of arteries and the choice of its mathematical expression. Am J Physiol Heart Circ Physiol. 1979;237:H620–31.

    CAS  Google Scholar 

  • Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Reading: Addison-Weseley; 1989.

    Google Scholar 

  • Green AE, Adkins JE. Large elastic deformations. 2nd ed. Oxford: Oxford University Press; 1970.

    Google Scholar 

  • Guo X, Lanir Y, Kassab GS. Effect of osmolarity on the zero-stress state and mechanical properties of aorta. Am J Physiol Heart Circ Physiol. 2007;293(4):H2328–34.

    Article  PubMed  CAS  Google Scholar 

  • Hollander Y, Durban D, Lu X, Kassab GS, Lanir Y. Constitutive modeling of coronary arterial media: comparison of three model classes. J Biomech Eng. 2011a;133(6):0610008.

    Article  Google Scholar 

  • Hollander Y, Durban D, Lu X, Kassab GS, Lanir Y. Experimentally validated microstructural 3D constitutive model of coronary arterial media. J Biomech Eng. 2011b;133(3):031007.

    Google Scholar 

  • Holzapfel GA, Gasser TC. Computational stress-deformation analysis of arterial walls including high pressure response. Int J Cardiol. 2007;116(1):78–85.

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

  • Holzapfel GA, Gasser TC, Stadler M. A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element simulation. Eur J Mech A Solids. 2002;21(3):441–63.

    Article  Google Scholar 

  • Holzapfel GA, Gasser TC, Ogden RW. Comparison of a multi-layer structural model for arterial walls with a fung-type model, and issues of material stability. J Biomech Eng. 2004a;126:264–75.

    Article  PubMed  Google Scholar 

  • Holzapfel GA, Sommer G, Regitnig P. Anisotropic mechanical properties of tissue components in human atherosclerosis plaques. J Biomech Eng. 2004b;126:657–65.

    Article  PubMed  Google Scholar 

  • Holzapfel GA, Sommer G, Gasser CT, Regitnig P. Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerosis intimal thickening and related constitutive modeling. Am J Physiol Heart Circ Physiol. 2005;289:2048–58.

    Article  Google Scholar 

  • Humphrey JD. Mechanics of the arterial wall: review and directions. Crit Rev Biomed Eng. 1995;23(1–2):1–162.

    PubMed  CAS  Google Scholar 

  • Humphrey JD. Cardiovascular solid mechanics: cells, tissues, and organs. New York: Springer; 2002.

    Book  Google Scholar 

  • Humphrey JD. Review paper: continuum biomechanics of soft biological tissues. Proc R Soc Lond A. 2003;459(2029):3–46.

    Article  Google Scholar 

  • Humphrey JD, Strumpf RK, Yin FC. A theoretically-based experimental approach for identifying vascular constitutive relations. Biorheology. 1989;26(4):687–702.

    PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Lanir Y. Mechanisms of residual stress in soft tissues. J Biomech Eng. 2009;131(4):044506.

    Article  PubMed  Google Scholar 

  • Lanir Y, Hayam G, Abovsky M, Zlotnick Y, Uretzky G, Nevo E, Ben-Haim SA. Effect of myocardial swelling on residual strain in the left ventricle of the rat. Am J Physiol Heart Circ Physiol. 1996;39:H1736–43.

    Google Scholar 

  • Lokshin O, Lanir Y. Micro and macro rheology of planar tissues. Biomaterials. 2009;30(17):3118–27.

    Article  PubMed  CAS  Google Scholar 

  • Lu X, Yang J, Zhao JB, Gregersen H, Kassab GS. Shear modulus of porcine coronary artery: contributions of media and adventitia. Am J Physiol Heart Circ Physiol. 2003;285:1966–75.

    Article  Google Scholar 

  • Nevo E, Lanir Y. Structural finite deformation model of the left ventricle during diastole and systole. J Biomech Eng. 1989;111(4):342–9.

    Article  PubMed  CAS  Google Scholar 

  • O’Connell MK, Murthy S, Phan S, Xu C, Buchanan J, Spilker R, Dalman RL, Zarins CK, Denk W, Taylor CA. The three-dimensional micro- and nanostructure of the aortic medial lamellar unit measured using 3d confocal and electron microscopy imaging. Matrix Biol. 2008;27(3):171–81.

    Article  PubMed  PubMed Central  Google Scholar 

  • Vaishnav RN, Young JT, Janicki JS, Patel DJ. Nonlinear anisotropic elastic properties of the canine aorta. Biophys J. 1972;12(8):1008–27.

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Wang C, Garcia M, Lu X, Lanir Y, Kassab GS. Three-dimensional mechanical properties of porcine coronary arteries: a validated two-layer model. Am J Physiol Heart Circ Physiol. 2006;291(3):H1200–9.

    Article  PubMed  CAS  Google Scholar 

  • Wasano K, Yamamoto T. Tridimensional architecture of elastic tissue in the rat aorta and femoral artery—a scanning electron microscope study. J Electron Microsc (Tokyo). 1983;32(1):33–44.

    CAS  Google Scholar 

  • Wolinsky H, Glagov S. A lamellar unit of aortic medial structure and function in mammals. Circ Res. 1967;20:99–111.

    Article  PubMed  CAS  Google Scholar 

  • Zulliger MA, Fridez P, Hayashi K, Stergiopulos N. A strain energy function for arteries accounting for wall composition and structure. J Biomech. 2004;37(7):989–1000.

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ghassan S. Kassab .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Hollander, Y., Durban, D., Lu, X., Kassab, G.S., Lanir, Y. (2016). Structure-Based Constitutive Model of Coronary Media. In: Kassab, G., Sacks, M. (eds) Structure-Based Mechanics of Tissues and Organs. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7630-7_13

Download citation

Publish with us

Policies and ethics