Three-dimensional stress and strain distribution in a two-layer model of a coronary artery

Springer Science and Business Media LLC - Tập 23 - Trang 49-55 - 2009
Keiichi Takamizawa1
1Department of Biomedical Engineering, Advanced Medical Engineering Center, National Cardiovascular Center Research Institute, Suita, Japan

Tóm tắt

For a right coronary artery, three-dimensional stress and strain distributions at a physiological intraluminal pressure and an axial extension ratio were computed on the basis of a two-layer elastic model. To validate the model, curves of external radius versus pressure and of axial force versus pressure were computed for three axial extension ratios. To analyze mechanical properties, stress-free configurations of media and adventitia, and the constitutive law of each layer in literature, were used. The present study showed that the peak circumferential stress and the peak axial stress appear in the media at the boundary between the media and adventitia. This result is due to the opening angle of the media being larger than π (rad) and the larger value of a material constant of the strain energy function for the media than for the adventitia. The circumferential stress and strain were discontinuous at the boundary. On the other hand, the radial stress was continuous at the boundary because of the boundary condition for stress. The circumferential stress and axial stress in the adventitia were almost uniformly distributed, and smaller than in the media. The residual stress and strain were also computed. The circumferential residual stress and strain were almost linearly distributed in each layer, although discontinuity appeared at the boundary between the two layers.

Tài liệu tham khảo

Carew TE, Vaishnav RN, Patel DJ. Compressibility of the arterial wall. Circ Res. 1968;23:61–8. Chuong CJ, Fung YC. Three-dimensional stress distribution in arteries. J Biomech Eng. 1983;105:268–74. Chuong CJ, Fung YC. Compressibility and constitutive relation of arterial wall in radial compression experiments. J Biomech. 1984;17:35–40. Chuong CJ, Fung YC. On residual stress in arteries. J Biomech Eng. 1986;108:189–92. Chuong CJ, Fung YC. Residual stress in arteries. In: Schmid-schönbein GW, Woo SL-Y, Zweifach BW, editors. Frontiers in Biomechanics. New York: Springer-Verlag; 1986. p. 117–29. Fung YC. What principle governs the stress distribution in living organs? In: Fung YC, Fukada E, Junjian W, editors. Biomechanics in China, Japan and USA. Beijing: Science Press; 1983. p. 1–13. Fung YC. Biodynamics: circulation. New York: Springer-Verlag; 1984. Fung YC, Fronec K, Patitucci P. Pseudoelasticity of arteries and the choice of its mathematical expression. Am J Physiol. 1979;237:H620–31. Fung YC, Liu SQ. Change of zero-stress state of rat pulmonary arteries in hypoxic hypertension. J Appl Physiol. 1991;70:2455–70. Guo X, Lu X, Kassab GS. Transmural strain distribution in the blood vessel wall. Am J Physiol. 2005;288:H881–6. Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elasticity. 2000;61:1–48. Holzapfel GA, Sommer G, Gasser CT, Regitnig P. Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling. Am J Physiol. 2005;289:H2048–58. Humphrey JD. Cardiovascular solid mechanics. New York: Springer-Verlag; 2002. Liu SQ, Fung YC. Zero-stress states of arteries. J Biomech Eng. 1988;110:82–4. Lu X, Pandit A, Kassab GS. Biaxial incremental homeostatic elastic moduli of coronary artery: two-layer model. Am J Physiol. 2004;287:H1663–9. Matsumoto T, Hayashi K. Stress and strain distribution in hypertensive and normotensive rat aorta considering residual strain. J Biomech Eng. 1996;118:62–73. Matsumoto T, Sato M. Analysis of stress and strain distribution in the artery wall consisted of layers with different elastic modulus and opening angle. JSME Int J Ser C. 2002;45:906–12. Rachev A. Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertension conditions. J Biomech. 1997;30:819–27. Takamizawa K, Hayashi K. Strain energy density function and uniform strain hypothesis for arterial mechanics. J Biomech. 1987;20:7–17. Takamizawa K, Hayashi K. Uniform strain hypothesis and thin-walled theory in arterial mechanics. Biorheology. 1988;25:555–65. Vaishnav RN, Vossoughi J. Estimations of residual strains in aortic segments. In: Hall CW, editor. Biomedical engineering II, recent developments. New York: Pergamon Press; 1983. p. 330–3. Vaishnav RN, Vossoughi J. Residual stress and strain in aortic segments. J Biomech. 1987;20:235–9. Vaishnav RN, Young JT, Patel DJ. Distribution of stresses and of strain-energy density through the wall thickness in a canine aortic segment. Circ Res. 1973;32:577–83. von Maltzhan WW, Warriyar RG, Keitzer WF. Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J Biomech. 1984;17:839–47. Wang C, Garcia M, Lu X, Laniar Y, Kassab GS. Three-dimensional mechanical properties of porcine coronary arteries: a validated two-layer model. Am J Physiol. 2006;291:H1200–9. Wang C, Zhang W, Kassab GS. The validation of a generalized Hooke’s law for coronary arteries. Am J Physiol. 2008;294:H66–73.