Passive mechanical properties and constitutive modeling of blood vessels in relation to microstructure | Medical & Biological Engineering & Computing Skip to main content
Springer Nature Link
Log in

Passive mechanical properties and constitutive modeling of blood vessels in relation to microstructure

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

Mechanical property variations of blood vessels from different anatomical sites supposedly reflect variations in microstructure, but no explicit association has been afforded so far. The objective of the present study was to provide precise histometrical and mechanical data, allowing the identification of such an association for arteries and veins. For biomechanical characterization, a one-dimensional (1D) constitutive model was developed adopting a ‘Fung-type’ exponential function to reproduce the stiffening effect of blood vessels at high stresses and combining it with a power function to reproduce the low-stress response. Histometrical studies were conducted with quantification of fiber composition and waviness for the entire vessel and its layers. Significant correlations were found between the model parameters and extracellular matrix organization. The novel model associates with recently-derived strain-energy functions for the arterial wall, provides powerful fit to uniaxial tension data from all types of vascular tissue studied, and conforms explicitly to microstructure.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Carboni M, Desch GW, Weizsacker HW (2007) Passive mechanical properties of porcine left circumflex artery and its mathematical description. Med Eng Phys 29:8–16

    Article  Google Scholar 

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

    Google Scholar 

  3. Desch GW, Weizsacker HW (2007) A model for passive elastic properties of rat vena cava. J Biomech 40:3130–3145

    Article  Google Scholar 

  4. Dobrin PB, Canfield TR (1984) Elastase, collagenase, and the biaxial elastic properties of dog carotid artery. Am J Physiol 247:H124–H131

    Google Scholar 

  5. Dobrin PB (1999) Distribution of lamellar deformations: Implications for properties of the arterial media. Hypertension 33:806–810

    Google Scholar 

  6. Driessen NJ, Bouten CV, Baaijens FP (2005) A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution. J Biomech Eng 127:494–503

    Article  Google Scholar 

  7. Fonck E, Prod’hom G, Roy S et al (2007) Effect of elastin degradation on carotid wall mechanics as assessed by a constituent-based biomechanical model. Am J Physiol Heart Circ Physiol 292:H2754–H2763

    Article  Google Scholar 

  8. Fung YC (1973) Biorheology of soft tissues. Biorheology 10:139–155

    Google Scholar 

  9. Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York

    Google Scholar 

  10. 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 

  11. Hasegawa M (1983) Rheological properties and wall structures of large veins. Biorheology 20:531–545

    Google Scholar 

  12. Hayashi K (1994) Experimental approaches on measuring the mechanical properties and constitutive laws of arterial walls. J Biomech Eng 115:481–488

    Article  Google Scholar 

  13. Holzapfel GA, Weizsacker HW (1998) Biomechanical behavior of the arterial wall and its numerical characterization. Comput Biol Med 28:377–392

    Article  Google Scholar 

  14. 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  MATH  MathSciNet  Google Scholar 

  15. Humphrey JD (2002) Cardiovascular solid mechanics: cells, tissues, and organs. Springer, New York

    Google Scholar 

  16. Kitoh T, Kawai Y, Ohhashi T (1993) Effects of collagenase, elastase, and hyaluronidase on mechanical properties of isolated dog jugular veins. Am J Physiol 265:H273–H280

    Google Scholar 

  17. Lillie MA, Gosline JM (2006) Tensile residual strains on the elastic lamellae along the porcine thoracic aorta. J Vasc Res 43:587–601

    Article  Google Scholar 

  18. Medynsky AO, Holdsworth DW, Sherebrin MH et al (1998) The effect of storage time and repeated measurements on the elastic properties of isolated porcine aortas using high resolution X-ray CT. Can J Physiol Pharmacol 76:451–456

    Article  Google Scholar 

  19. Monson KL, Goldsmith W, Barbaro NM et al (2005) Significance of source and size in the mechanical response of human cerebral blood vessels. J Biomech 38:737–744

    Article  Google Scholar 

  20. Moreno AH, Katz AI, Gold LD et al (1970) Mechanics of distension of dog veins and other very thin-walled tubular structures. Circ Res 27:1069–1080

    Google Scholar 

  21. Nichols WW, O’Rourke MF (2005) McDonald’s blood flow in arteries. Theoretical experimental and clinical principles. Oxford University Press, New York

    Google Scholar 

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

    Article  Google Scholar 

  23. Sakanishi A, Hasegawa M, Dobashi T (1988) Distensibility characteristics of caval veins and empirical exponential formulae. Biorheology 25:165–172

    Google Scholar 

  24. Samila ZJ, Carter SA (1981) The effect of age on the unfolding of elastin lamellae and collagen fibers with stretch in human carotid arteries. Can J Physiol Pharmacol 59:1050–1057

    Google Scholar 

  25. Silver FH, Snowhill PB, Foran DJ (2003) Mechanical behavior of vessel wall: a comparative study of aorta, vena cava, and carotid artery. Ann Biomed Eng 31:793–803

    Article  Google Scholar 

  26. Snowhill PB, Foran DJ, Silver FH (2004) A mechanical model of porcine vascular tissues-part I: determination of macromolecular component arrangement and volume fractions. Cardiovasc Eng 4:281–294

    Article  Google Scholar 

  27. Sokolis DP, Boudoulas H, Karayannacos PE (2002) Assessment of the aortic stress–strain relation in uniaxial tension. J Biomech 35:1213–1223

    Article  Google Scholar 

  28. Sokolis DP, Zarbis N, Dosios T et al (2005) Post-vagotomy mechanical characteristics and structure of the thoracic aortic wall. Ann Biomed Eng 33:1504–1516

    Article  Google Scholar 

  29. Sokolis DP, Kefaloyannis EM, Kouloukoussa M et al (2006) A structural basis for the aortic stress-strain relation in uniaxial tension. J Biomech 39:1651–1662

    Article  Google Scholar 

  30. Sokolis DP (2007) Three-part passive constitutive laws for the aorta in simple elongation. J Med Eng Technol 31:397–409

    Article  Google Scholar 

  31. VanBavel E, Siersma P, Spaan JAE (2003) Elasticity of passive blood vessels: a new concept. Am J Physiol Heart Circ Physiol 285:H1986–H2000

    Google Scholar 

  32. Vito RP, Dixon SA (2003) Blood vessel constitutive models: 1995–2002. Ann Rev Biomed Eng 5:413–439

    Article  Google Scholar 

  33. Wolinsky H, Glagov S (1964) Structural basis for the static mechanical properties of the aortic media. Circ Res 14:400–413

    Google Scholar 

  34. Xie JP, Liu SQ, Yang RF et al (1991) The zero-stress state of rat veins and vena cava. J Biomech Eng 113:36–41

    Article  Google Scholar 

  35. Yamada H (1970) Strength of biological materials. Williams & Wilkins, Baltimore

    Google Scholar 

  36. Zulliger MA, Fridez P, Hayashi K et al (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. Laboratory of Biomechanics, Foundation of Biomedical Research, Academy of Athens, 11527, Athens, Greece

    Dimitrios P. Sokolis

  2. 35, Lefkados St., 15354, Athens, Greece

    Dimitrios P. Sokolis

Authors
  1. Dimitrios P. Sokolis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dimitrios P. Sokolis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sokolis, D.P. Passive mechanical properties and constitutive modeling of blood vessels in relation to microstructure. Med Biol Eng Comput 46, 1187–1199 (2008). https://doi.org/10.1007/s11517-008-0362-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-008-0362-7

Keywords

Search

Navigation