Skip to main content
Log in

Layer-Specific 3D Residual Deformations of Human Aortas with Non-Atherosclerotic Intimal Thickening

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Data relating to residual deformations in human arteries are scarce. In this paper we investigate three-dimensional residual deformations for intact strips and for their separate layers from human aortas in their passive state. From 11 abdominal aortas with identified anamnesis, 16 pairs of rings and axial strips were harvested, and the rings cut open. After 16 h images of the resulting geometries were recorded, and the strips were separated into their three layers; after another 6 h images were again recorded. Image processing and analysis was then used to quantify residual stretches and curvatures. For each specimen histological analysis established that the intima, media and adventitia were clearly separated, and the separation was atraumatic. Axial in situ stretches were determined to be 1.196 ± 0.084. On separation, the strips from the adventitia and media shortened (between 4.03 and 8.76% on average), while the intimal strips elongated on average by 3.84% (circumferential) and 4.28% (axial) relative to the associated intact strips. After separation, the adventitia from the ring sprang open by about 180° on average, becoming flat, the intima opened only slightly, but the media sprang open by more than 180° (as did the intact strip). The adventitia and intima from the axial strips remained flat, while the media (and the intact strip) bent away from the vessel axis. This study has shown that residual deformations are three dimensional and cannot be described by a single parameter such as ‘the’ opening angle. Their quantification and modeling therefore require consideration of both stretching and bending, which are highly layer-specific and axially dependent.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.

Similar content being viewed by others

References

  1. Badrek-Amoudi A., Patel C. K., Kane T. P. C., Greenwald S. E. (1996) The effect of age on residual strain in the rat aorta. J. Biomech. Eng. 118:440–444

    Google Scholar 

  2. Bergel, D. H. The visco-elastic properties of the arterial wall. Ph.D. thesis, University of London, 1960.

  3. Bergel, D. H. The properties of blood vessels. In: Fung Y. C., Perrone N., Anliker M. (eds) Biomechanics: Its Foundations and Objectives. Prentice-Hall, Englewood Cliffs, New Jersey, pp 105–139, 1972.

  4. Cabrera Fischer E. I., Bia D., Camus J. M., Zocalo Z., Forteza E., Armentano R. L. (2006) Adventitia-dependent mechanical properties of brachiocephalic ovine arteries in in vivo and in vitro studies. Acta Physiol. 188:103–111

    Article  CAS  Google Scholar 

  5. Chuong C. J., Fung Y. C. (1983) Three-dimensional stress distribution in arteries. J. Biomech. Eng. 105:268–274

    PubMed  CAS  Google Scholar 

  6. Chuong C. J., Fung Y. C. (1986) On residual stress in arteries. J. Biomech. Eng. 108:189–192

    PubMed  CAS  Google Scholar 

  7. Cox R. H. (1974) Three-dimensional mechanics of arterial segments in vitro: Methods. J. Appl. Phys. 36:381–384

    CAS  Google Scholar 

  8. Dobrin, P. B. Vascular mechanics. In: Shepherd J. T., Abboud F. M. (eds) Handbook of Physiology Section 2: The Cardiovascular System, volume III. American Physiological Society, Bethesda, pp 65–102, 1983.

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

    PubMed  CAS  Google Scholar 

  10. Fung Y.C. (1983) On the foundations of biomechanics. J. Appl. Mech. 50:1003–1009

    Article  Google Scholar 

  11. Fung Y. C., Liu S. Q. (1989) Change of residual strains in arteries due to hypertrophy caused by aortic constrictions. Circ. Res. 65:1340–1349

    PubMed  CAS  Google Scholar 

  12. Fung Y. C., Liu S. Q. (1989) Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction. J. Biomech. Eng. 111:325–335

    PubMed  Google Scholar 

  13. Fung, Y. C. and S. Q. Liu. Strain distribution in small blood vessels with zero-stress state taken into consideration. Am. J. Physiol. H544–H552, 1992.

  14. Gonzalez R. C., Woods R. E. (1992) Digital Image Processing. Addison Wesley, New York

    Google Scholar 

  15. Greenwald S. E., Moore J. E. Jr., Rachev A., Kane T. P. C., Meister J.-J. (1997) Experimental investigation of the distribution of residual strains in the artery wall. J. Biomech. Eng. 119:438–444

    PubMed  CAS  Google Scholar 

  16. Holzapfel G. A., Gasser T. C., Ogden R. W. (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity 61:1–48

    Article  Google Scholar 

  17. Holzapfel G. A., Gasser T. C., Ogden R. W. (2004) Comparison of a multi-layer structural model for arterial walls with a Fung-type model, and issues of material stability. J. Biomech. Eng. 126:264–275

    Article  PubMed  Google Scholar 

  18. Holzapfel, G. A. and R. W. Ogden (eds). Mechanics of Biological Tissue. Springer-Verlag, Heidelberg, 2006.

  19. Holzapfel G. A., Sommer G., Gasser C. T., and Regitnig P. (2005) Determination of the layer-specific mechanical properties of human coronary arteries with non-atherosclerotic intimal thickening, and related constitutive modelling. Am. J. Physiol. Heart Circ. Physiol. 289:H2048–H2058

    Article  PubMed  CAS  Google Scholar 

  20. Humphrey J. D. (2002) Cardiovascular Solid Mechanics. Cells, Tissues, and Organs. Springer-Verlag, New York

    Google Scholar 

  21. Humphrey J. D., Yin F. C. P. (1989) Constitutive relations and finite deformations of passive cardiac tissue: II. Stress analysis in the left ventricle. Circ. Res. 65:805–817

    PubMed  CAS  Google Scholar 

  22. Liu S.Q., Fung Y.C. (1988) Zero-stress states of arteries. J. Biomech. Eng. 110:82–84

    Article  PubMed  CAS  Google Scholar 

  23. Lohn M., Dubrovska G., Lauterbach B., Luft F. C., Gollasch M., Sharma A. M. (2002) Periadventitial fat releases a vascular relaxing factor. FASEB J. 16:1057–1063

    Article  PubMed  Google Scholar 

  24. Matsumoto T., Hayashi K. (1996) Stress and strain distribution in hypertensive and normotensive rat aorta considering residual strain. J. Biomech. 118:62–73

    CAS  Google Scholar 

  25. Matsumoto T., Hayashi K., Ide K. (1995) Residual strain and local strain distributions in the rabbit atherosclerotic aorta. J. Biomech. 28:1207–1217

    Article  PubMed  CAS  Google Scholar 

  26. von Maltzahn W.-W., Warriyar R. G., Keitzer W. F. (1984) Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J. Biomech. 17:839–847

    Article  Google Scholar 

  27. McDonald D. A. (1974) Bloodflow in Arteries. Edward Arnold, London

    Google Scholar 

  28. Nichols W. W., O’Rourke M. F. (1998) McDonald’s Blood Flow in Arteries. Theoretical, Experimental and Clinical Principles, Chapter 4, 4th edition. Arnold, London, pp. 73–97.

    Google Scholar 

  29. Ogden, R. W. and C. A. J. Schulze-Bauer. Phenomenological and structural aspects of the mechanical response of arteries. In: Mechanics in Biology, edited by J. Casey, and G. Bao. New York: The American Society of Mechanical Engineers (ASME), AMD-Vol. 242/BED-Vol. 46, 2000, pp. 125–140.

  30. Patel D. J., Vaishnav R. N. (1980) Basic Hemodynamics and its Role in Disease Processes. University Park Press, Baltimore

    Google Scholar 

  31. Rachev A., Greenwald S. E. (2003) Residual strains in conduit arteries. J. Biomech. 36:661–670

    Article  PubMed  CAS  Google Scholar 

  32. Saini A., Berry C., Greenwald S. (1995) Effect of age and sex on residual stress in the aorta. J. Vasc. Res. 32:398–405

    PubMed  CAS  Google Scholar 

  33. Schulze-Bauer C. A. J., Mörth C., Holzapfel G. A. (2003) Passive biaxial mechanical response of aged human iliac arteries. J. Biomech. Eng. 125:395–406

    Article  PubMed  Google Scholar 

  34. Schulze-Bauer C. A. J., Regitnig P., Holzapfel G. A. (2002) Mechanics of the human femoral adventitia including high-pressure response. Am. J. Physiol. Heart Circ. Physiol. 282:H2427–H2440

    PubMed  CAS  Google Scholar 

  35. Stary H. C. (2003) Atlas of Atherosclerosis: Progression and Regression, 2nd edition The Parthenon Publishing Group Limited, Boca Raton, London, New York, Washington, DC

    Google Scholar 

  36. Stary, H. C., D. H. Blankenhorn, A. B. Chandler, S. Glagov, W. Insull, Jr., M. Richardson, M. E. Rosenfeld, S. A. Schaffer, C. J. Schwartz, W. D. Wagner, and R. W. Wissler. A definition of the intima of human arteries and of its atherosclerosis-prone regions. A report from the committee on vascular lesions of the council on arteriosclerosis, american heart association. Circulation 85:391–405, 1992.

    Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  38. Takamizawa K., Hayashi K. (1988) Uniform strain hypothesis and thin-walled theory in arterial mechanics. Biorheology 25:555–565

    PubMed  CAS  Google Scholar 

  39. Vaishnav R. N., Vossoughi J. (1983) Estimation of residual strains in aortic segments. In: Hall C. W. (ed.) Biomedical Engineering II: Recent Developments. Pergamon Press, New York, pp 330–333

    Google Scholar 

  40. Vito R. P. (1973) A note on arterial elasticity. J. Biomech. 6:561–564

    Article  PubMed  CAS  Google Scholar 

  41. Vossoughi, J. Longitudinal residual strains in arteries. In: Proceedings of the 11th Southern Biomedical Engineering Conference, Memphis, TN, 1992. October 2–4, 1992, pp. 17–19.

  42. Vossoughi, J., Z. Hedjazi, and F. S. Borris. Intimal residual stress and strain in large arteries. In: Proceedings of the Summer Bioengineering Conference, edited by N. A. Langrana, M. H. Friedman, and E. S. Groods. New York: ASME, 1993, pp. 434–437.

  43. Weizsäcker H. W., Lambert H., Pascale K. (1983) Analysis of the passive mechanical properties of rat carotid arteries. J. Biomech. 16:703–715

    Article  PubMed  Google Scholar 

  44. Weizsäcker H. W., Pinto J. G. (1988) Isotropy and anisotropy of the arterial wall. J. Biomech. 21:477–487

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

The authors are indebted to the late C.A.J. Schulze-Bauer and to E. Pernkopf, who helped to initiate the early part of this work and made substantial contributions to the experiments. Financial support for this research was partly provided by the ‘Fonds zur Fortsetzung Christian’s Forschung’, the Austrian Science Foundation under START-Award Y74-TEC and by the Oesterreichische Nationalbank (OeNB) project 9190. These supports are gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gerhard A. Holzapfel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Holzapfel, G.A., Sommer, G., Auer, M. et al. Layer-Specific 3D Residual Deformations of Human Aortas with Non-Atherosclerotic Intimal Thickening. Ann Biomed Eng 35, 530–545 (2007). https://doi.org/10.1007/s10439-006-9252-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-006-9252-z

Keywords

Navigation