Comparison of a Multi-Layer Structural Model for Arterial Walls with a Fung-Type Model, and Issues of Material Stability

Journal of Biomechanical Engineering

Volumn 126, Issue 2, 2004, Pages 264-275

  Holzapfel, Gerhard A ^a   Gasser, Thomas C ^a   Ogden, Ray W ^b  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; ELASTICITY; FINITE ELEMENT METHOD; MULTILAYERS; STRAIN;

ARTERIAL WALLS; ARTERIES; MATERIAL PARAMETERS; MATERIAL STABILITY;

BIOMECHANICS;

ANISOTROPY; ARTERY WALL; ARTICLE; BIOMECHANICS; CAROTID ARTERY; ELASTICITY; FINITE ELEMENT ANALYSIS; FUNG TYPE STRAIN ENERGY FUNCTION; GEOMETRY; MATHEMATICAL MODEL; MECHANICAL STRESS;

ANIMALS; ARTERIES; BLOOD PRESSURE; COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT ANALYSIS; MODELS, CARDIOVASCULAR; RABBITS; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; STRESS, MECHANICAL;

EID: 2442708176     PISSN: 01480731     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1695572     Document Type: Article

References (42)

1. Humphrey, J. D., 1995, "Mechanics of the Arterial Wall: Review and Directions," Crit. Rev. Biomed. Eng., 23, pp. 1-162.
2. Humphrey, J. D., 2002, Cardiovascular Solid Mechanics. Cells, Tissues, and Organs, Springer-Verlag, New York.
3. Holzapfel, G. A., Gasser, T. C., and Ogden, R. W., 2000, "A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models," J. Elasticity, 61, pp. 1-48.
4. Humphrey, J. D., 1999, "An Evaluation of Pseudoelastic Descriptors Used in Arterial Mechanics," J. Biomech. Eng., 121, pp. 259-262.
5. Horgan, C. O., and Saccomandi, G., 2003, "A Description of Arterial Wall Mechanics Using Limiting Chain Extensibility Constitutive Models," Biomech. Model. Mechanobio., 1, pp. 251-266.
6. Rhodin, J. A. G., 1980, "Architecture of the Vessel Wall." Handbook of Physiology, The Cardiovascular System, edited by D. F. Bohr, A. D. Somlyo, and H. V. Sparks, 2. American Physiologial Society. Bethesda, Maryland, pp. 1-31.
7. Xie, J., Zhou, J., and Fung, Y. C., 1995, "Bending of Blood Vessel Wall: Stress-Strain Laws of the Intima-Media and Adventitia Layers," J. Biomech. Eng., 117, pp. 136-145.
8. Holzapfel, G. A., Schulze-Bauer, C. A. J., and Stadler, M., 2000, "Mechanics of Angioplasty: Wall, Balloon and Stent," Mechanics in Biology. edited by J. Casey and G. Bao, The American Society of Mechanical Engineers (ASME), New York. AMD-Vol. 242/BED-Vol. 46, pp. 141-156.
9. Holzapfel, G. A., 2001, "Biomechanics of Soft Tissue," The Handbook of Materials Behavior Models. Volume III. Multiphysics Behaviors, Chapter 10, Composite Media, Biomaterials, edited by J. Lemaitre, Academic Press, Boston, pp. 1049-1063.
10. Chuong, C. J., and Fung, Y. C., 1983, "Three-Dimensional Stress Distribution in Arteries," J. Biomech. Eng., 105, pp. 268-274.
11. Fung, Y. C., Fronek, K., and Patitucci, P., 1979, "Pseudoelasticity of Arteries and the Choice of its Mathematical Expression," Am. J. Physiol., 237, pp. H620-H631.
12. Spencer, A. J. M., 1984, "Constitutive Theory for Strongly Anisotropic Solids," Continuum Theory of the Mechanics of Fibre-Reinforced Composites, edited by A. J. M. Spencer, Springer-Verlag, Wien, pp. 1-32, CISM Courses and Lectures No. 282, International Center for Mechanical Sciences.
13. Carew, T. E., Vaishnav, R. N., and Patel, D. J., 1968, "Compressibility of the Arterial Wall," Circ. Res., 23, pp. 61-68.
14. Ogden, R. W., 1997, Non-linear Elastic Deformations, Dover, New York.
15. Holzapfel, G. A., 2000, Nonlinear Solid Mechanics. A Continuum Approach for Engineering, John Wiley & Sons, Chichester.
16. Criscione, J. C., McCulloch, A. D., and Hunter, W. C., 2002, "Constitutive Framework Optimized for Myocardium and Other High-Strain, Laminar Materials With One Fiber Family," J. Mech. Phys. Solids, 50, pp. 1681-1702.
17. Holzapfel, G. A., Gasser, T. C., and Stadler, M., 2002, "A Structural Model for the Viscoelastic Behavior of Arterial Walls: Continuum Formulation and Finite Element Analysis." Eur. J. Mech. A/Solids, 21, pp. 441-463.
18. Deng, S. X., Tomioka, J., Debes, J. C., and Fung, Y. C., 1994, "New Experiments on Shear Modulus of Elasticity of Arteries," Am. J. Physiol., 266, pp. H1-H10.
19. Maltzahn, W.-W. V., Warriyar, R. G., and Keitzer, W. F., 1984, "Experimental Measurements of Elastic Properties of Media and Adventitia of Bovine Carotid Arteries," J. Biomech., 17, pp. 839-847.
20. Kang, T., Humphrey, J. D., and Yin, F. C. P., 1996, "Comparison of Biaxial Mechanical Properties of Excised Endocardium and Epicardium," Am. J. Physiol., 270, pp. H2169-H2176.
21. Kas'yanov, V. A., and Rachev, A. I., 1980, "Deformation of Blood Vessels Upon Stretching, Internal Pressure, and Torsion," Mech. Comp. Mat., 16, pp. 76-80.
22. Holzapfel, G. A., Eberlein, R., Wriggers, P., and Weizsäcker, H. W., 1996, "A new Axisymmetrical Membrane Element for Anisotropic, Finite Strain Analysis of Arteries," Comput. Methods Appl. Mech. Eng., 12, pp. 507-517.
23. Roach, M. R., and Burton, A. C., 1957, "The Reason for the Shape of the Distensibility Curve of Arteries," Canad. J. Biochem. Physiol., 35, pp. 681-690.
24. Holzapfel, G. A., and Gasser, T. C., 2001, "A Viscoelastic Model for Fiber-Reinforced Composites at Finite Strains: Continuum Basis, Computational Aspects and Applications," Comput. Methods Appl. Mech. Eng., 190, pp. 4379-4403.
25. Gasser, T. C., and Holzapfel, G. A., 2002, "A Rate-Independent Elastoplastic Constitutive Model for (Biological) Fiber-Reinforced Composites at Finite Strains: Continuum Basis, Algorithmic Formulation and Finite Element Implementation," Comput. Mech., 29, pp. 340-360.
26. Schulze-Bauer, C. A. J., Mörth, C., and Holzapfel, G. A., 2003, "Passive Biaxial Mechanical Response of Aged Human Iliac Arteries," J. Biomech. Eng., 125, pp. 395-406.
27. Schulze-Bauer, C. A. J., and Holzapfel, G. A., 2003, "Determination of Constitutive Equations for Human Arteries From Clinical Data," J. Biomech., 36, pp. 185-169.
28. Yu, Q., Zhou, J., and Fung, Y. C., 1993, "Neutral Axis Location in Bending and Young's Modulus of Different Layers of Arterial Wall," Am. J. Physiol., 265, pp. H52-H60.
29. Finlay, H. M., McCullough, L., and Canham, P. B., 1995, "Three-Dimensional Collagen Organization of Human Brain Arteries at Different Transmural Pressures," J. Vasc. Res., 32, pp. 301-312.
30. Choung, C. J., and Fung, Y. C., 1986, "On Residual Stresses in Arteries," J. Biomech. Eng., 108, pp. 189-192.
31. Billiar, K. L., and Sacks, M. S., 1997, "A Method to Quantify the Fiber Kinematics of Planar Tissues Under Biaxial Stretch," J. Biomech., 30, pp. 753-756.
32. Elbischger, P. J., Bischof, H., Regitnig, P., and Holzapfel, G. A., "Automatic Analysis of Collagen Fiber Orientation in the Outermost Layer of Human Arteries." submitted.
33. Fung, Y. C., 1993, Biomechanics. Mechanical Properties of Living Tissues, Springer-Verlag, New York, 2nd ed.
34. Schulze-Bauer, C. A. J., Regitnig, P., and Holzapfel, G., 2002, "Mechanics of the Human Femoral Adventitia Including High-Pressure Response," Am. J. Physiol. Heart Circ. Physiol., 282, pp. H2427-2440.
35. Ogden, R. W., 2001, "Elements of the Theory of Finite Elasticity," Nonlinear Elasticity. Theory and Applications, edited by Y. B. Fu and R. W. Ogden, Cambridge University Press, Cambridge, pp. 1-57.
36. Zee, L., and Sternberg, E., 1983, "Ordinary and Strong Ellipticity in the Equilibrium Theory of Incompressible Hyperelastic Solids," Arch. Ration. Mech. Anal., 83, pp. 53-90.
37. Wilber, J. P., and Walton, J. R., 2002, "The Convexity Properties of a Class of Constitutive Models for Biological Soft Tissue's," Math. Mech. Solids, 7, pp. 217-235.
38. Abeyaratne, R. C., 1980, "Discontinuous Deformation Gradients in Plane Finite Elastostatics of Incompressible Materials," J. Elasticity, 10, pp. 255-293.
39. Merodio, J., and Ogden, R. W., 2002, "Material Instabilities in Fiber-Reinforced Nonlinearly Elastic Solids Under Plane Deformation," Arch. Mech., 54, pp. 525-552.
40. Horgan, C. O., and Saccomandi, G., 2002, "Constitutive Modelling of Rubber-Like and Biological Materials With Limiting Chain Extensibility," Math. Mech. Solids, 7, pp. 353-371.
41. Hill, R., 1968, "On Constitutive Inequalities for Simple Materials-I," J. Mech. Phys. Solids, 16, pp. 229-242.
42. Hill, R., 1968, "On Constitutive Inequalities for Simple Materials-II," J. Mech. Phys. Solids, 16, pp. 315-322.