Stress and Strain Analyses of Blood Vessels in Physiological and Pathological Conditions

  • Hiroshi Yamada


Boundary-value problems of blood vessels are formulated and solved with a finite element method. In the mathematical modeling, constitutive equations were formulated as a hyperelastic material for blood vessels and other tissues based on a finite deformation theory. For boundary-value problems of vasculature, three cases are chosen as physiologically or pathologically typical conditions. One is the case of an artery in which smooth muscles are activated. The pressure-diameter relationship, stress distribution and opening angle change are predicted in various active conditions. The second is the case of a coronary vessel in the myocardium. The effects of the deformation of surrounding tissues and the location of the blood vessel are examined through analysis. The third case is the pathological case of an abdominal aortic aneurysm. In this case, the geometrical effect on the risk of rupture of the aneurysm is estimated through stress analysis by assuming various initial geometries.


Abdominal Aortic Aneurysm Hydraulic Resistance Smooth Muscle Contraction Passive State Transmural Pressure 
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  1. Azuma T, Hasegawa M (1971) A Theological approach to the architecture of arterial walls. Jpn J Physiol 21: 27 - 47CrossRefGoogle Scholar
  2. Cox RH (1978) Regional variation of series elasticity in canine arterial smooth muscles. Am J Physiol 234: H542 - H551Google Scholar
  3. Matsumoto T, Tsuchida M, Sato M (1996) Change in intramural strain distribution in rat aorta due to smooth muscle contraction and relaxation. Am J Physiol 271: H1711 - H1716Google Scholar
  4. Murphy RA (1976) Contractile system function in mammalian smooth muscle. Blood Vessels 13: 1 - 23Google Scholar
  5. Price JM, Davis DL, Knauss EB (1981), Length-dependent sensitivity in vascular smooth muscle. Am J Physiol 241: H557 - H563Google Scholar
  6. Racev A, Hayashi K (1999) Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distribution in arteries. Annals Biomed Eng 27: 459 - 468CrossRefGoogle Scholar
  7. Roach MR (1957) The reason for the shape of the distensibility curves of arteries. Can J Biochem Physiol 35: 681 - 690CrossRefGoogle Scholar
  8. Sipkema P, Yamada H, Yin FCP (1996) Coronary artery resistance changes depend on how surrounding myocardial tissue is stretched. Am J Physiol 270: H924 - H934Google Scholar
  9. Smail B, Hunter P (1991) Structure and function of the diastolic heart: Material properties of passive myocardium. In: Glass L, Hunter P, McCulloch A (eds) Theory of heart. Springer, New York, pp 1 - 29Google Scholar
  10. Yamada H, Shinoda T, Tanaka E, Yamamoto S (1999) Finite element modeling and numerical simulation of the artery in active state. JSME Int J Ser C 42: 501 - 507CrossRefGoogle Scholar
  11. Yamada H, Sipkema P, Yin F (1996) Mechanical effect of surrounding lipid layer and myocardial tissue on hydraulic resistance of canine coronary artery (in Japanese). Trans Jpn Soc Mech Eng Ser A 62: 2838 - 2845.CrossRefGoogle Scholar
  12. Yamada H, Tanaka E, Murakami S (1992) Mechanical evaluation for the growth and rupture of aneurysm in abdominal aorta (in Japanese). Trans Jpn Soc Mech Eng Ser A 58: 1087 - 1092CrossRefGoogle Scholar
  13. Yamada H, Tanaka E, Murakami S (1994) Mechanical evaluation for the growth and rupture of aneurysm in abdominal aorta. JSME Int J Ser A 37: 181 - 187Google Scholar

Copyright information

© Springer Japan 2000

Authors and Affiliations

  • Hiroshi Yamada
    • 1
  1. 1.Department of Micro System Engineering, Graduate School of EngineeringNagoya UniversityNagoyaJapan

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