Arterial growth and remodelling is driven by hemodynamics

  • Luca Cardamone
  • Jay D. Humphrey
Part of the MS&A — Modeling, Simulation and Applications book series (MS&A, volume 5)


Experimental observations highlight the importance of altered hemodynamics on arterial function and adaptation [27, 28, 29]. We discuss a class of mechano-biological models for growth and remodelling (G&R) of the arterial wall that describe the intimate interaction between hemodynamics, cell activity, and arterial wall mechanics. For some applications the artery can be described as a thin walled structure: for example, basic adaptations to perturbed pressure and flow, cerebral aneurysms, and vasospasms have been successfully modelled treating the vascular wall as a membrane. A multiple-time scales membrane model is described and illustrative results discussed. Future patient-specific models of large arteries and pathologies as atherosclerosis and abdominal aortic aneurysms require a full 3D model of the interaction between the blood flow and the growing vessel. We discuss the extension of the model to thick walled vessels and some preliminary results.


Wall Shear Stress Cardiac Cycle Deformation Gradient Strain Energy Density Blood Flow Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Alastrué V., Peña E., Martínez M.A., Doblaré M.: Assessing the use of the “opening angle method” to enforce resdidual stresses in patient–specific arteries. Ann. Biomed. Eng. 35: 1821–1837, 2007.CrossRefGoogle Scholar
  2. 2.
    Alford P.W., Humphrey J.D., Taber L.A.; Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents. Biomech. Mod. Mechanobiol. 7: 245–262, 2008.CrossRefGoogle Scholar
  3. 3.
    Baek S., Gleason R.L., Rajagopal K.R., Humphrey J.D.: Theory of small on large: Potential utility in computations of fluid–solid interactions in arteries. Comput. Methods Appl. Mech. Engrg. 196: 3070–3078, 2007.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Baek S., Rajagopal K.R., Humphrey J.D.: A theoretical model of enlarging intracranial fusiform aneurysms. J. Biomech. Eng. 128(1): 142–9, 2006.CrossRefGoogle Scholar
  5. 5.
    Baek S., Valentín A., Humphrey J.D.: Biochemomechanics of cerebral vasospasm and its resolution: II. constitutive relations and model simulations. Ann. Biomed. Eng. 35(9): 1498–1509, 2007.CrossRefGoogle Scholar
  6. 6.
    Burton A.C.: Relation of structure to function of the tissues of the wall of blood vessels. Physiol. Rev. 34: 619–642, 1954.Google Scholar
  7. 7.
    Cardamone L., Valentín A., Eberth J.F., Humphrey J.D.: Origin of axial prestretch and residual stress in arteries. Biomech. Mod. Mechanobiol. 8: 431–446, 2009.CrossRefGoogle Scholar
  8. 8.
    Cardamone L., Valentín A., Eberth J.F., Humphrey J.D.: Modeling carotid artery adaptations to dynamic alterations in pressure and flow over the cardiac cycle. Math. Med. Biol. 2010.Google Scholar
  9. 9.
    Dancu M.B., Berardi D.E., Vanden Heuvel J.P., Tarbell J.M.: Asynchronous shear stress and circumferential strain reduces endothelial NO synthase and cyclooxygenase-2 but induces endothelin-1 gene expression in endothelial cells. Arterioscler. Thromb. Vasc. Biol. 24: 2088–2094, 2004.CrossRefGoogle Scholar
  10. 10.
    Davis E.C.: Elastic lamina growth in the developing mouse aorta. J. Histochem. Cytochem. 43: 1115–1123, 1995.CrossRefGoogle Scholar
  11. 11.
    Demiray H.: Wave propagation through a viscous fluid contained in a prestressed thin elastic tube. Int. J. Eng. Sci. 30(11): 1607–1620, 1992.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Di Carlo A., Quiligotti S.: Growth and balance. Mech. Res. Comm. 29: 449–456, 2002.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Doblaré M. et al.: Anisotropic bone remodelling model based on a continuum damage-repair theory. Journal of Biomechanics 35(1): 1–17, 2002.CrossRefGoogle Scholar
  14. 14.
    Dobrin P.B., Canfield T., Sinha S.: Development of longitudinal retraction of carotid arteries in neonatal dogs. Experientia 31: 1295–1296, 1975.CrossRefGoogle Scholar
  15. 15.
    Eberth J.F., Gresham V.C., Reddy A.K., Popovic N., Wilson E., Humphrey J.D.: Importance of pulsatility in hypertensive carotid artery growth and remodeling. J. Hypertension 27: 2010–2021, 2009.CrossRefGoogle Scholar
  16. 16.
    Feldman S.A., Glagov S.: Transmural collagen and elastin in human aortas: reversal with age. Atherosclerosis 13: 385–394, 1971.CrossRefGoogle Scholar
  17. 17.
    Figueroa C.A., Baek S., Taylor C.A., Humphrey J.D.: A computational framework for fluidsolid-growth modeling in cardiovascular simulations. Computer Methods in Applied Mechanics and Engineering 198(45–46): 3583–3602, 2009.MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Gasser T., Ogden R., Holzapfel G.: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal of the Royal Society Interface 3(6): 15, 2006.CrossRefGoogle Scholar
  19. 19.
    Greenwald S.: Ageing of the conduit arteries. The Journal of Pathology 211(2): 157–172, 2007.CrossRefGoogle Scholar
  20. 20.
    Humphrey J.D.: Cardiovascular Solid Mechanics: Cells, Tissues, and Organs. Springer–Verlag, New York, 2002.Google Scholar
  21. 21.
    Humphrey J.D., Baek S., Niklason L.E.: Biochemomechanics of cerebral vasospasm and its resolution: I. a new hypothesis and theoretical framework. Ann. Biomed. Eng. 35(9): 1485–1497, 2007.CrossRefGoogle Scholar
  22. 22.
    Humphrey J.D., Na S.: Elastodynamics and arterial wall stress. Ann. Biomed. Eng. 30(4): 509–23, 2002.CrossRefGoogle Scholar
  23. 23.
    Humphrey J.D., Rajagopal K.R.: A constrained mixture model for growth and remodeling of soft tissues. Math. Models. Methods. Appl. Sci. 128(3): 407–30, 2002.MathSciNetCrossRefGoogle Scholar
  24. 24.
    Humphrey J.D., Rajagopal K.R.: A constrained mixture model for arterial adaptations to a sustained step change in blood flow. Biomech. Mod. Mechanobiol. 22: 109–126, 2003.CrossRefGoogle Scholar
  25. 25.
    Karšaj I., Humphrey J.: A mathematical model of evolving mechanical properties of intraluminal thrombus. Biorheology 46(6): 509–527, 2009.Google Scholar
  26. 26.
    Langille B.L.: Arterial remodeling: relation to hemodynamics. Can. J. Physiol. Pharmacol. 74(7): 834–41, 1996.CrossRefGoogle Scholar
  27. 27.
    Langille B.L., Bendeck M.P., Keeley F.W.: Adaptations of carotid arteries of young and mature rabbits to reduced carotid blood flow. Am. J. Physiol. 256(4 Pt 2): H931–9, 1989.Google Scholar
  28. 28.
    Langille B.L., O’Donnell F.: Reductions in arterial diameter produced by chronic decreases in blood flow are endothelium-dependent. Science 231(4736): 405–407, 1986.CrossRefGoogle Scholar
  29. 29.
    Malek A., Izumo S.: Physiological fluid shear stress causes downregulation of endothelin-1 mRNA in bovine aortic endothelium. Am. J. Physiol. 263(2 Pt 1): C389–96, 1992.Google Scholar
  30. 30.
    Matsumoto T., Hayashi K.: Stress and strain distribution in hypertensive and normotensive rat aorta considering residual strain. J. Biomech. Eng. 118(1): 62–73, 1996.CrossRefGoogle Scholar
  31. 31.
    Rizvi M.A.D., Katwa L., Spadone D.P., Myers P.R.: The effects of endothelin-1 on collagen type I and type III synthesis in cultured porcine coronary artery vascular smooth muscle cells. J. Mol. Cell Cardiol. 28(2): 243–252, 1996.CrossRefGoogle Scholar
  32. 32.
    Rizvi M.A.D., Myers P.R.: Nitric oxide modulates basal and endothelin-induced coronary artery vascular smooth muscle cell proliferation and collagen levels. J. Mol. Cell Cardiol. 27(7): 1779–1789, 1997.CrossRefGoogle Scholar
  33. 33.
    Rodbard S.: Vascular caliber. Cardiology 60(1): 4–49, 1975.CrossRefGoogle Scholar
  34. 34.
    Taber L.A.: A model for aortic growth based on fluid shear and fiber stresses. J. Biomech. Eng. 120(3): 348–54, 1998.CrossRefGoogle Scholar
  35. 35.
    Taber L.A., Humphrey J.D.: Stress-modulated growth, residual stress, and vascular heterogeneity. J. Biomech. Eng. 123: 528–535, 2001.CrossRefGoogle Scholar
  36. 36.
    Tada S., Tarbell J.M.: A computational study of flow in a compliant carotid bifurcation-stress phase angle correlation with shear stress. Ann. Biomed. Eng. 33(9): 1202–1212, 2005.CrossRefGoogle Scholar
  37. 37.
    Valentín A., Cardamone L., Baek S., Humphrey J.D.: Complementary vasoactivity and matrix remodeling in arterial adaptations to altered flow and pressure. J. Roy. Soc. Interface 6: 293–306, 2009.CrossRefGoogle Scholar
  38. 38.
    Valentín A., Humphrey J.: Modeling effects of axial extension on arterial growth and remodeling. Medical and Biological Engineering and Computing 47(9): 979–987, 2009.CrossRefGoogle Scholar
  39. 39.
    Zamir M.: The Physics of Pulsatile Flow. Springer, New York, 2000.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  1. 1.Sector of Functional Analysis and ApplicationsSISSA—International School for Advanced StudiesTriesteItaly
  2. 2.Department of Biomedical EngineeringYale UniversityNew Haven, ConnecticutUSA

Personalised recommendations