Skip to main content
SpringerLink
Log in

A Model of Arterial Adaptation to Alterations in Blood Flow

  • Chapter
Cardiovascular Soft Tissue Mechanics

Abstract

Mechanisms of arterial adaptation to changes in blood flow rates were tested by comparing the predictions of a proposed theoretical model with available experimental data. The artery was modeled as an elastic membrane made of a nonlinear, incompressible, elastic material. Stimulation of the vascular smooth muscle was modeled through the generation of an active component of circumferential stress. The muscular tone was modulated by flow-induced shear stress sensed by the arterial endothelium, and is responsible for the vasomotor adjustment of the deformed arterial diameter in response to changes in blood flow. This study addresses the hypothesis that the synthetic and proliferative activity of smooth muscle cells, leading to a change in arterial dimensions, is shear stress dependent and is associated with changes in the contractile state of the smooth muscle cells and changes in the circumferential wall stress. Remodeling to a step change in flow was formulated as an initial-value problem for a system of first order autonomous differential equations for the evolution of muscular tone and evolution of arterial geometry. The governing equations were solved numerically for model parameters identified from experimental data available in the literature. The model predictions for the time variation of the geometrical dimensions and their asymptotic values were found to be in qualitative agreement with available experimental data. Experiments for validating the introduced hypotheses and further generalizations of the model were discussed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Achakri, A. Rachev, N. Stergiopulos and J.-J. Meister, A theoretical investigation of low frequency diameter oscillations of muscular arteries. Ann. Biomedical Eng. 22 (1994) 253–263.

    Google Scholar 

  2. G.L. Baumbach and D.D. Heistad, Remodeling of cerebral arterioles in chronic hypertension. Hypertension 13 (1989) 968–972.

    Google Scholar 

  3. J.A. Beven and I. Laher, Pressure and flow-dependent vascular tone. FASEB J. 5 (1991) 2267–2273.

    Google Scholar 

  4. N. Brady, R. Merval, J. Benessiano, J.-L. Samuel and A. Tedgul, Differential effects of pressure and flowon DNA and protein synthesis and on fibrinectin expression by arteries in a novel organ culture system. Circ. Res. 77 (1995) 684–694.

    Google Scholar 

  5. J.E. Brayden, Membrane hyperpolarization is a mechanism of endothelium-dependent cerebral vasodilatation. Am. J. Physiol. 259 (1990) 668–673.

    Google Scholar 

  6. R.D. Brownlee and B.L. Langille, Arterial adaptation to altered blood flow. Canad. J. Physiol. Parmacol. 69 (1991) 978–983.

    Google Scholar 

  7. J. Chamley-Campbell, G.R. Campbell and R. Ross, The smooth muscle cell in culture. Physiol. Rev. 59 (1979) 1–61.

    Google Scholar 

  8. A. Cho, L. Mitchell, D. Koopmans and B.L. Langille, Effects of changes in blood flow rate on cell death and cell proliferation in carotid arteries of immature rabbits. Circ. Res. 81(3) (1997) 328–337.

    Google Scholar 

  9. CJ. Chuong and Y.C. Fung, On residual stress in arteries. ASME J. Biomech. Eng. 108 (1986) 189–192.

    Article  Google Scholar 

  10. R.H. Cox, Comparision of carotid artery mechanics in the rat, rabbit, and dog. Am. J. Physiol. 234 (1978) 280–288.

    Google Scholar 

  11. R.H. Cox, Regional variation of series elasticity in canine arterial smooth muscles. Am. J. Physiol. 234 (1978) 542–551.

    Google Scholar 

  12. H. Demiray, H.W. Weizacker and K. Pascale, A mechanical model for passive behavior of rats carotid artery. In: Biomedizinische Technik, Band 31, Heft 3 (1986), pp. 46–52.

    Google Scholar 

  13. P.B. Dobrin, Isometric and isobaric contraction of carotid arterial smooth muscle. Am. J. Physiol. 225 (1973) 659–663.

    Google Scholar 

  14. RB. Dobrin, Influence of initial length on length-tension relationship of vascular smooth muscle. Am. J. Physiol. 225 (1973) 664–670.

    Google Scholar 

  15. RB. Dobrin, Vascular mechanics. In: D.F. Bohr, A.R Somlyo and H.V. Sparks Jr. (eds), Handbook of Physiology. The Cardiovascular System. Vascular Smooth Muscle, Am. Physiol. Soc., Bethesda (1983), Chapter 3, pp. 65–104.

    Google Scholar 

  16. P.B. Dobrin and A.A. Rovick, Influence of vascular smooth muscle on contractile mechanisms and elasticity of arteries. Am. J. Physiol. 217 (1969) 1644–1651.

    Google Scholar 

  17. I. Di Stefano, D.R. Koopmans and B.L. Langille, Modulation of arterial growth of the rabbit carotid artery associated with experimental elevation of blood flow. J. Vase. Res. 1 (1998) 1–7.

    MATH  Google Scholar 

  18. A. Ben Driss, J. Benessiano, P. Poitevin, B.I. Levy and J.B. Michel, Arterial expansive remodeling induced by high flow rates. Am. J. Physiol. 272 (1997) 851–858.

    Google Scholar 

  19. W. Path, H.M. Burkhart, S.C. Miller, M.C. Dalshing and J.L. Unthank, Wall remodeling after wall shear rate normalization in rat mesenteric colaterals. J. Vas. Res. 35 (1998) 257–264.

    Google Scholar 

  20. Y.C. Fung, Biodynamics: Circulation, Springer-Verlag, New York (1984).

    Google Scholar 

  21. Y.C. Fung, Biomechanics: Motion, Flow, Stress, and Growth, Springer-Verlag, New York (1990).

    MATH  Google Scholar 

  22. Y.C. Fung and P. Patitucci, Pseudoelasticity of arteries and choice of its mathematical expressions. Am. J. Physiol. 35 (1979) 620–631.

    Google Scholar 

  23. W.R. Hume, Proline and thymidineuptake in rabbit ear artery segments in vitro increased by chronic tangential load. Hypertension 2 (1980) 738–743.

    Google Scholar 

  24. C.W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Inc., Englewood Cliffs, NJ (1971).

    MATH  Google Scholar 

  25. S. Glagov, C.K. Zarnis, N. Masawa, C.P. Xu, H. Bassiouny and D.P. Giddens, Mechanical functional role of non-atherosclerotic intimal thickening. Frontiers Med. Biol. Engng. 1 (1993) 37–43.

    Google Scholar 

  26. B.S. Gow, The influence of vascular smooth muscle on the viscoelastic properties of blood vessels. In: D. Bergel (ed.), Cardiovascular Fluid Dynamics, Academic Press (1972), pp. 65–110.

    Google Scholar 

  27. A.E. Green and J.E. Adkins, Large Elastic Deformations and Non-Linear Continuum Mechanics, Clarendon Press, Oxford (1960).

    MATH  Google Scholar 

  28. J.R. Guyton and C.J. Hartley, Flow restriction of one carotid artery in juvenile rats inhibits growth of arterial diameter. Am. J. Physiol. 248 (1985) 54–546.

    Google Scholar 

  29. L. Kaiser, S.S. Hull Jr. and H.V. Sparks Jr., Methylene blue and ETYA block flow-dependent dilation in canine femoral artery. Am. J. Physiol. 250 (1986) 974–981.

    Google Scholar 

  30. A. Kamiya and T. Togawa, Adaptive regulation of wall shear stress to flow change in canine carotid artery. Am. J. Physiol. 239 (1980) 14–21.

    Google Scholar 

  31. D.N. Ku and R.C. Allen, Vascular grafts. In: J.D. Bronzino (ed.), The Biomedical Engineering Handbook, CRC Press (1995), pp. 1871–1878.

    Google Scholar 

  32. B.L. Langille, Remodeling of developing and mature arteries: Endothelium, smooth muscle and matrix. J. Cardiovasc. Pharmacol. 21 (Suppl. 1) (1993) 11–17.

    Google Scholar 

  33. B.L. Langille, Blood flow-induced remodeling of the artery wall. In: J.A. Bevan, G. Kaley and G. Rubanyi (eds), Flow-Dependent Regulation of Vascular Function, Oxford University Press, New York (1995), pp. 227–299.

    Google Scholar 

  34. B.L. Langille, M.P., Bendeck and W. Keeley, Adaptations of carotid arteries of young and mature rabbits to reduced carotid blood flow. Am. J. Physiol. 256 (1989) 931–939.

    Google Scholar 

  35. B.L. Langille and F. O’Donnell, Reductions in arterial diameter produced by chronic decrease in blood flow are endothelium-dependent. Science Wash. DC 231 (1986) 405–407.

    Google Scholar 

  36. D.Y.M. Leung, S.G. Glagov and M.B. Mathews, Cycling stretching stimulates synthesis of components by arterial smooth muscle cells in vivo. Science 116 (1976) 455–477.

    Google Scholar 

  37. S. Lehoux and A. Tedgui, Signal transduction of mechanical stresses in the vascular wall. Hypertension 32 (1998) 338–345.

    Google Scholar 

  38. Sir J. Lighthill, Mathematical Biofliuddynamics, Society for Industrial and Applied Mathematics, Philadelphia, PA (1975).

    Google Scholar 

  39. H. Masuda, H. Bassiouny, S. Glagov and C.K. Zarins, Artery wall restructuring in response to increased flow. Surg. Forum 40 (1989) 285–286.

    Google Scholar 

  40. H. Masuda, K. Kawamura, T. Sugiyama and A. Kamiya, Effects of endothelial denudationin flow-induced arterial dilatation. Frontiers. Med. Biol. Engng. 1 (1993) 57–62.

    Google Scholar 

  41. T. Matsumoto, E. Okumura, Y. Miura and M. Sato, Mechanical and dimensional adaptation on rabbit carotid artery cultured in vitro. Mech. Biol. Eng. Comput. 37 (1999) 252–256.

    Google Scholar 

  42. G.K. Owens, Role of mechanical strain in regulation of differentiation of vascular muscle cells. Circ. Res. 79 (1996) 1054–1055.

    Google Scholar 

  43. F. Pourageaud and J.G. De Mey, Structural properties of rat mesenteric small arteries after 4-wk exposure to elevated or reduced blood flow. Am. J. Physiol. 273 (1997) 1699–1706.

    Google Scholar 

  44. C.M. Quick, H.L. Baldick, N. Safabakhsh, T.J. Lenihan, K.-J.J. Li, H.W. Weizsacker and A. Noordergraaf, Unstable radii in muscular blood vessels. Am. J. Physiol. 271 (1996) 2669–2676.

    Google Scholar 

  45. A. Rachev, Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertensive conditions. J. Biomechanics 8 (1997) 819–827.

    Google Scholar 

  46. A. Rachev, Ts. Ivanov and K. Boev, A model for contraction of smooth muscle. Mech. Comp. Mat. 2 (1980) 259–263 (translated from Russian).

    Google Scholar 

  47. A. Rachev and K. Hayashi, Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Ann. Biomedical Eng. 27 (1999) 459–468.

    Google Scholar 

  48. A. Rachev, N. Stergiopulos and J.-J. Meister, Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressures. J. Biomechanic 5 (1996) 635–642.

    Google Scholar 

  49. A. Rachev, N. Stergiopulos and J.-J. Meister, Amodel for geometrical and mechanical adaptation of arteries to sustained hypertension. ASME J. Biomech. Eng. 120 (1998) 9–17.

    Google Scholar 

  50. H. Rausmussen and P. Barrett, Calcium messenger system: An integrated view. Physiol. Rev. 64 (1984) 938–984.

    Google Scholar 

  51. C.M. Rembold and R.A. Murphy, Latch-bridge model in smooth muscle:/Ca2+l1 can quantitatively predict stress. Am. J. Physiol. 259 (1990) C251–C259.

    Google Scholar 

  52. P. Reusch, H. Wagdy, R. Reusch, E. Wilson and H. Ives, Mechanical strain increases smooth muscle and decreases nonmuscle myosin expression in rat vascular smooth muscle cells. Circ. Res. 79 (1996) 1046–1053.

    Google Scholar 

  53. W. Risau, Vasculogennesis, angiogenesis, and endothelial cell differentiation during embryonic development. In: R.N. Feinberg, G.K. Sherer and R. Auerach (eds), The Development of the Vascular System, Karger, Basel (1991), pp. 58–68.

    Google Scholar 

  54. S. Rodbard, Negative feedback mechanisms in the architecture and function of the connective and cardiovascular tissue. Perspectives in Biology and Medicine 13 (1970) 507–527.

    Google Scholar 

  55. E.K. Rodriguez, A. Hoger and A.D. McCulloch, Stress-dependent finite growth in soft elastic tissues. J. Biomechanics 27 (1994) 455–467.

    Google Scholar 

  56. L.A. Taber, A theoretical study of aortic growth. In: Advances in Bioengineering, BED-Vol. 28, ASME (1994), pp. 1–2.

    Google Scholar 

  57. L.A. Taber, Biomechanical growth laws for muscle tissue. J. Theor. Biol. 193(2) (1998) 201–213.

    Article  MathSciNet  Google Scholar 

  58. L.A. Taber, A model for aortic growth based on fluid shear and fiber stresses. ASME J. Biomech. Eng. 120 (1998) 348–354.

    Google Scholar 

  59. L.A. Taber and D.W. Eggers, Theoretical study of stress-modulated growth in the aorta. J. Theoret. Biol. 180 (1996) 343–357.

    Google Scholar 

  60. A. Tulis, J.L. Unthank and R.L. Prewitt, Flow-induced arterial remodeling in rat mesenteric vasculature. Am. J. Physiol. 274 (1998) 874–882.

    Google Scholar 

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

    Google Scholar 

  62. E. Wilson, Q. Mai, K. Sudhir, R.H. Weiss and H.E. Ives, Mechanical strain induces growth of vascular smooth muscle cells via autocrine action of PDFG. J. Cell Biol. 123 (1993) 741–747.

    Article  Google Scholar 

  63. L.C. Wong and B.L. Langille, Developmental remodeling of the internal elastic lamina of rabbit arteries: Effect of blood flow. Circ. Res. 78(5) (1996) 799–805.

    Google Scholar 

  64. P.J. Zeller and T.C. Skalak, Contribution of individual structural components in determining the zero-stress state in small arteries. J. Vasc. Res. 35 (1998) 8–17.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Alexander Rachev

Authors
  1. Alexander Rachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering New York Center for Biomedical Engineering, The City College, New York, USA

    Stephen C. Cowin

  2. Department of Biomedical Engineering, Texas A&M University, College Station, TX, USA

    Jay D. Humphrey

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Kluwer Academic Publishers

About this chapter

Cite this chapter

Rachev, A. (2001). A Model of Arterial Adaptation to Alterations in Blood Flow. In: Cowin, S.C., Humphrey, J.D. (eds) Cardiovascular Soft Tissue Mechanics. Springer, Dordrecht. https://doi.org/10.1007/0-306-48389-0_3

Download citation

  • DOI: https://doi.org/10.1007/0-306-48389-0_3

  • Received:

  • Revised:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0220-5

  • Online ISBN: 978-0-306-48389-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation